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NEWEST QUESTIONS
The number of solutions of 2 x p x + k = y 2. Let's consider the family of diophantine equations. 2 x p x + k = y 2. being p > 2 a prime and k a positive integer. An example is given by the equation. 2 x ⋅ 3 x + 97 = y 2. that presents, at least, nt.number-theory prime-numbers diophantine-equations. NEWEST 'COMPLEX-GEOMETRY' QUESTIONS The period map and the Kodaira--Spencer map. Let f: X → B be a non-isotrivial holomorphic submersion with connected fibres between compact Kähler manifolds of positive relative dimension. Suppose the fibres of f are Calabi--Yau $ (c_ {1,\ ag.algebraic-geometry complex-geometry deformation-theory kahler-manifolds. FA.FUNCTIONAL ANALYSIS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
OPEN PROBLEMS WITH MONETARY REWARDS A. Bressan has advertised two monetary rewards of $500 each for solutions to problems on mixing flows and blocking problems. The first problem was unsolved as of Jan. 15, 2011, although progress in relevant directions is noted in the linked announcement. The second problem was announced on Jan. 19, 2011. Share. RA.RINGS AND ALGEBRAS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
HOMOLOGICAL ALGEBRA
Excercise 2.2.1 in Weibel ("An Introduction to Homological Algebra") states that an object P in the category of chain complexes over an abelian category is projective if and only it is a split exact complex of projectives. I was able to solve the only-if-part but I have touble with the if-part and would be glad if someone can give me some help.NT.NUMBER THEORY
t ). b) Comparing π ( x) and Li ( x). All the numerical data shows π ( x) < Li ( x), and Gauss thought this was always true, but in 1914 Littlewood used the Riemann hypothesis to show the inequality reverses infinitely often. In 1933, Skewes used RH to show the inequality reverses for some x below 10^10^10^34.PR.PROBABILITY
I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis' 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading. HOMOTOPY PULLBACK IN THE CATEGORY OF DG ALGEBRAS I was wondering if somebody could tell me the definition of homotopy pullback. Suppose $\def\C{{\cal C}}\C$ is a relative category, i.e., a category equipped with a subcategory, morphisms in which are known as weak equivalences.For example, take the category of MATHOVERFLOWQUESTIONSUNANSWERED MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up. Sign up to jointhis community
NEWEST QUESTIONS
The number of solutions of 2 x p x + k = y 2. Let's consider the family of diophantine equations. 2 x p x + k = y 2. being p > 2 a prime and k a positive integer. An example is given by the equation. 2 x ⋅ 3 x + 97 = y 2. that presents, at least, nt.number-theory prime-numbers diophantine-equations. NEWEST 'COMPLEX-GEOMETRY' QUESTIONS The period map and the Kodaira--Spencer map. Let f: X → B be a non-isotrivial holomorphic submersion with connected fibres between compact Kähler manifolds of positive relative dimension. Suppose the fibres of f are Calabi--Yau $ (c_ {1,\ ag.algebraic-geometry complex-geometry deformation-theory kahler-manifolds. FA.FUNCTIONAL ANALYSIS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
OPEN PROBLEMS WITH MONETARY REWARDS A. Bressan has advertised two monetary rewards of $500 each for solutions to problems on mixing flows and blocking problems. The first problem was unsolved as of Jan. 15, 2011, although progress in relevant directions is noted in the linked announcement. The second problem was announced on Jan. 19, 2011. Share. RA.RINGS AND ALGEBRAS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
HOMOLOGICAL ALGEBRA
Excercise 2.2.1 in Weibel ("An Introduction to Homological Algebra") states that an object P in the category of chain complexes over an abelian category is projective if and only it is a split exact complex of projectives. I was able to solve the only-if-part but I have touble with the if-part and would be glad if someone can give me some help.NT.NUMBER THEORY
t ). b) Comparing π ( x) and Li ( x). All the numerical data shows π ( x) < Li ( x), and Gauss thought this was always true, but in 1914 Littlewood used the Riemann hypothesis to show the inequality reverses infinitely often. In 1933, Skewes used RH to show the inequality reverses for some x below 10^10^10^34.PR.PROBABILITY
I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis' 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading. HOMOTOPY PULLBACK IN THE CATEGORY OF DG ALGEBRAS I was wondering if somebody could tell me the definition of homotopy pullback. Suppose $\def\C{{\cal C}}\C$ is a relative category, i.e., a category equipped with a subcategory, morphisms in which are known as weak equivalences.For example, take the category ofNEWEST QUESTIONS
The number of solutions of 2 x p x + k = y 2. Let's consider the family of diophantine equations. 2 x p x + k = y 2. being p > 2 a prime and k a positive integer. An example is given by the equation. 2 x ⋅ 3 x + 97 = y 2. that presents, at least, nt.number-theory prime-numbers diophantine-equations.ASK A QUESTION
Ask a public question. Step 1: Draft your question. Step 2: Review your question. Title. Be specific and imagine you’re asking a question to another person. Similar questions. Body. Include all the information someone would need to answer your question. Thanks for contributing an answer to MathOverflow!PR.PROBABILITY
How to check positive-definiteness of this function? where S 1 is the 1-sphere S 1 = { s → ∈ R 2: s → 2 = 1 } and μ ( d s →) is a measure on S 1 ( μ ≥ 0 ). I know that ϕ is a characteristic function of some probability distribution*. Therefore, according to Bochner's theorem, ϕ is a AG.ALGEBRAIC GEOMETRY 10 hours ago · Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange AG.ALGEBRAIC GEOMETRY 1 Answer1. Suppose for simplicity X is proper. Choose a smooth simplicial resolution X ∙ → X. We can assume that X 0 → X is a resolution of singularities. By (a careful reading of) Deligne, Théorie de Hodge III, we have an exact sequence. where the second map is the difference of pullbacks along the structure maps X 1 → X 0 . AT.ALGEBRAIC TOPOLOGY 1 day ago · Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeREFERENCE REQUEST
1 day ago · Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange IS COHOMOLOGY ALWAYS RELATED TO TOPOLOGY? I am trying to understand whether there is a sense in which cohomology always relates to topology or whether this is the case only in particular examples. IS THERE A NICE Q-ANALOGUE OF THE JACOBI IDENTITY IN A 1 day ago · Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeST.STATISTICS
Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers tolearn, share
MATHOVERFLOWQUESTIONSUNANSWERED MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up. Sign up to jointhis community
NEWEST QUESTIONS
The number of solutions of 2 x p x + k = y 2. Let's consider the family of diophantine equations. 2 x p x + k = y 2. being p > 2 a prime and k a positive integer. An example is given by the equation. 2 x ⋅ 3 x + 97 = y 2. that presents, at least, nt.number-theory prime-numbers diophantine-equations. NEWEST 'COMPLEX-GEOMETRY' QUESTIONS The period map and the Kodaira--Spencer map. Let f: X → B be a non-isotrivial holomorphic submersion with connected fibres between compact Kähler manifolds of positive relative dimension. Suppose the fibres of f are Calabi--Yau $ (c_ {1,\ ag.algebraic-geometry complex-geometry deformation-theory kahler-manifolds. FA.FUNCTIONAL ANALYSIS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
OPEN PROBLEMS WITH MONETARY REWARDS A. Bressan has advertised two monetary rewards of $500 each for solutions to problems on mixing flows and blocking problems. The first problem was unsolved as of Jan. 15, 2011, although progress in relevant directions is noted in the linked announcement. The second problem was announced on Jan. 19, 2011. Share. RA.RINGS AND ALGEBRAS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
HOMOLOGICAL ALGEBRA
Excercise 2.2.1 in Weibel ("An Introduction to Homological Algebra") states that an object P in the category of chain complexes over an abelian category is projective if and only it is a split exact complex of projectives. I was able to solve the only-if-part but I have touble with the if-part and would be glad if someone can give me some help.NT.NUMBER THEORY
t ). b) Comparing π ( x) and Li ( x). All the numerical data shows π ( x) < Li ( x), and Gauss thought this was always true, but in 1914 Littlewood used the Riemann hypothesis to show the inequality reverses infinitely often. In 1933, Skewes used RH to show the inequality reverses for some x below 10^10^10^34.PR.PROBABILITY
I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis' 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading. HOMOTOPY PULLBACK IN THE CATEGORY OF DG ALGEBRAS I was wondering if somebody could tell me the definition of homotopy pullback. Suppose $\def\C{{\cal C}}\C$ is a relative category, i.e., a category equipped with a subcategory, morphisms in which are known as weak equivalences.For example, take the category of MATHOVERFLOWQUESTIONSUNANSWERED MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up. Sign up to jointhis community
NEWEST QUESTIONS
The number of solutions of 2 x p x + k = y 2. Let's consider the family of diophantine equations. 2 x p x + k = y 2. being p > 2 a prime and k a positive integer. An example is given by the equation. 2 x ⋅ 3 x + 97 = y 2. that presents, at least, nt.number-theory prime-numbers diophantine-equations. NEWEST 'COMPLEX-GEOMETRY' QUESTIONS The period map and the Kodaira--Spencer map. Let f: X → B be a non-isotrivial holomorphic submersion with connected fibres between compact Kähler manifolds of positive relative dimension. Suppose the fibres of f are Calabi--Yau $ (c_ {1,\ ag.algebraic-geometry complex-geometry deformation-theory kahler-manifolds. FA.FUNCTIONAL ANALYSIS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
OPEN PROBLEMS WITH MONETARY REWARDS A. Bressan has advertised two monetary rewards of $500 each for solutions to problems on mixing flows and blocking problems. The first problem was unsolved as of Jan. 15, 2011, although progress in relevant directions is noted in the linked announcement. The second problem was announced on Jan. 19, 2011. Share. RA.RINGS AND ALGEBRAS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
HOMOLOGICAL ALGEBRA
Excercise 2.2.1 in Weibel ("An Introduction to Homological Algebra") states that an object P in the category of chain complexes over an abelian category is projective if and only it is a split exact complex of projectives. I was able to solve the only-if-part but I have touble with the if-part and would be glad if someone can give me some help.NT.NUMBER THEORY
t ). b) Comparing π ( x) and Li ( x). All the numerical data shows π ( x) < Li ( x), and Gauss thought this was always true, but in 1914 Littlewood used the Riemann hypothesis to show the inequality reverses infinitely often. In 1933, Skewes used RH to show the inequality reverses for some x below 10^10^10^34.PR.PROBABILITY
I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis' 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading. HOMOTOPY PULLBACK IN THE CATEGORY OF DG ALGEBRAS I was wondering if somebody could tell me the definition of homotopy pullback. Suppose $\def\C{{\cal C}}\C$ is a relative category, i.e., a category equipped with a subcategory, morphisms in which are known as weak equivalences.For example, take the category ofNEWEST QUESTIONS
The number of solutions of 2 x p x + k = y 2. Let's consider the family of diophantine equations. 2 x p x + k = y 2. being p > 2 a prime and k a positive integer. An example is given by the equation. 2 x ⋅ 3 x + 97 = y 2. that presents, at least, nt.number-theory prime-numbers diophantine-equations.ASK A QUESTION
Ask a public question. Step 1: Draft your question. Step 2: Review your question. Title. Be specific and imagine you’re asking a question to another person. Similar questions. Body. Include all the information someone would need to answer your question. Thanks for contributing an answer to MathOverflow!PR.PROBABILITY
How to check positive-definiteness of this function? where S 1 is the 1-sphere S 1 = { s → ∈ R 2: s → 2 = 1 } and μ ( d s →) is a measure on S 1 ( μ ≥ 0 ). I know that ϕ is a characteristic function of some probability distribution*. Therefore, according to Bochner's theorem, ϕ is a AG.ALGEBRAIC GEOMETRY 3 hours ago · Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange AG.ALGEBRAIC GEOMETRY 1 Answer1. Suppose for simplicity X is proper. Choose a smooth simplicial resolution X ∙ → X. We can assume that X 0 → X is a resolution of singularities. By (a careful reading of) Deligne, Théorie de Hodge III, we have an exact sequence. where the second map is the difference of pullbacks along the structure maps X 1 → X 0 . AT.ALGEBRAIC TOPOLOGY 1 day ago · Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeREFERENCE REQUEST
1 day ago · Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange IS COHOMOLOGY ALWAYS RELATED TO TOPOLOGY? I am trying to understand whether there is a sense in which cohomology always relates to topology or whether this is the case only in particular examples. IS THERE A NICE Q-ANALOGUE OF THE JACOBI IDENTITY IN A 1 day ago · Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeST.STATISTICS
Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers tolearn, share
MATHOVERFLOWQUESTIONSUNANSWERED MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up. Sign up to jointhis community
NEWEST QUESTIONS
The number of solutions of 2 x p x + k = y 2. Let's consider the family of diophantine equations. 2 x p x + k = y 2. being p > 2 a prime and k a positive integer. An example is given by the equation. 2 x ⋅ 3 x + 97 = y 2. that presents, at least, nt.number-theory prime-numbers diophantine-equations.MATHOVERFLOW
Finding all proper divisors of a 3 z 3 + a 2 z 2 + a 1 z + 1 of the form x z + 1. nt.number-theory divisors-multiples. modified 29 mins ago David Jones 161. -1. votes. 0. answers. 61. views. FA.FUNCTIONAL ANALYSIS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
AT.ALGEBRAIC TOPOLOGY Let ( G, n) be a pair such that n is a natural number, G is a finite group which is abelian if n ≥ 1. It is well-known that π n ( K ( G, n)) = G and π i ( K ( G, n)) = 0 if i ≠ n. Also it is known that these spaces K ( G, n) play a very important role for cohomology. For any abelian group G, and any CW-complex X, the set [ X, K ( RA.RINGS AND ALGEBRAS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
HOMOLOGICAL ALGEBRA
Excercise 2.2.1 in Weibel ("An Introduction to Homological Algebra") states that an object P in the category of chain complexes over an abelian category is projective if and only it is a split exact complex of projectives. I was able to solve the only-if-part but I have touble with the if-part and would be glad if someone can give me some help. AG.ALGEBRAIC GEOMETRY Special values of L-functions as periods. If M is a pure motive over Q, one cas define its L -function L(M, s) which conjecturaly is a meromorphic function over C with finitely many poles. For example, when M = Q is the trivial motive, L(Q, s) is the Riemann Zeta function ζ(s). There is a famous concjecture saying that all values of L(M, s)at
HOMOTOPY PULLBACK IN THE CATEGORY OF DG ALGEBRAS I was wondering if somebody could tell me the definition of homotopy pullback. Suppose $\def\C{{\cal C}}\C$ is a relative category, i.e., a category equipped with a subcategory, morphisms in which are known as weak equivalences.For example, take the category ofPR.PROBABILITY
I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis' 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading. MATHOVERFLOWQUESTIONSUNANSWERED MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up. Sign up to jointhis community
NEWEST QUESTIONS
The number of solutions of 2 x p x + k = y 2. Let's consider the family of diophantine equations. 2 x p x + k = y 2. being p > 2 a prime and k a positive integer. An example is given by the equation. 2 x ⋅ 3 x + 97 = y 2. that presents, at least, nt.number-theory prime-numbers diophantine-equations.MATHOVERFLOW
Finding all proper divisors of a 3 z 3 + a 2 z 2 + a 1 z + 1 of the form x z + 1. nt.number-theory divisors-multiples. modified 29 mins ago David Jones 161. -1. votes. 0. answers. 61. views. FA.FUNCTIONAL ANALYSIS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
AT.ALGEBRAIC TOPOLOGY Let ( G, n) be a pair such that n is a natural number, G is a finite group which is abelian if n ≥ 1. It is well-known that π n ( K ( G, n)) = G and π i ( K ( G, n)) = 0 if i ≠ n. Also it is known that these spaces K ( G, n) play a very important role for cohomology. For any abelian group G, and any CW-complex X, the set [ X, K ( RA.RINGS AND ALGEBRAS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
HOMOLOGICAL ALGEBRA
Excercise 2.2.1 in Weibel ("An Introduction to Homological Algebra") states that an object P in the category of chain complexes over an abelian category is projective if and only it is a split exact complex of projectives. I was able to solve the only-if-part but I have touble with the if-part and would be glad if someone can give me some help. AG.ALGEBRAIC GEOMETRY Special values of L-functions as periods. If M is a pure motive over Q, one cas define its L -function L(M, s) which conjecturaly is a meromorphic function over C with finitely many poles. For example, when M = Q is the trivial motive, L(Q, s) is the Riemann Zeta function ζ(s). There is a famous concjecture saying that all values of L(M, s)at
HOMOTOPY PULLBACK IN THE CATEGORY OF DG ALGEBRAS I was wondering if somebody could tell me the definition of homotopy pullback. Suppose $\def\C{{\cal C}}\C$ is a relative category, i.e., a category equipped with a subcategory, morphisms in which are known as weak equivalences.For example, take the category ofPR.PROBABILITY
I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis' 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading. HOTTEST QUESTIONS THIS WEEK What is the involution on the moduli space of genus 3 curves induced by the Torelli map. ag.algebraic-geometry algebraic-curves abelian-varieties jacobians. answered May 26 at 23:07 Dan Petersen35.1k. 3.
ASK A QUESTION
Ask a public question. Step 1: Draft your question. Step 2: Review your question. Title. Be specific and imagine you’re asking a question to another person. Similar questions. Body. Include all the information someone would need to answer your question. Thanks for contributing an answer to MathOverflow! AG.ALGEBRAIC GEOMETRY 1 Answer1. Suppose for simplicity X is proper. Choose a smooth simplicial resolution X ∙ → X. We can assume that X 0 → X is a resolution of singularities. By (a careful reading of) Deligne, Théorie de Hodge III, we have an exact sequence. where the second map is the difference of pullbacks along the structure maps X 1 → X 0 .NT.NUMBER THEORY
nt.number theory - L-function terminology - MathOverflow. 2. Let E / F be a quadratic extension of two number fields. Denote by f the conductor of E / F and let χ be the primitive Hecke Grossencharacter mod f associated to the non-trivial character of the abelian group G a l ( E / F) = Z / 2 Z.REFERENCE REQUEST
1 day ago · Question: On balance, with theoretical advances in algorithmic information theory and Quantum Computation it appears that the remarkable effectiveness of mathematics is AT.ALGEBRAIC TOPOLOGY Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
OPEN PROBLEMS WITH MONETARY REWARDS A. Bressan has advertised two monetary rewards of $500 each for solutions to problems on mixing flows and blocking problems. The first problem was unsolved as of Jan. 15, 2011, although progress in relevant directions is noted in the linked announcement. The second problem was announced on Jan. 19, 2011. Share. HOW DO WE STUDY IWASAWA THEORY? The specific example that Iwasawa studied was the p -Sylow subgroup of the class group of K n = Q ( ζ p n). It's naturally a Z p -module as well as a G n = Gal ( K n / K 1) -module, but the group ring Z p isn't very nice; it's not a domain, for instance. If we instead look at the inverse limits of the pSHEAF THEORY
A map F → G of PSh(X) is said to be a local isomorphism if for every point x ∈ X, the induced map Fx → Gx on stalks is a bijection. Denote by W the class of local isomorphisms. Now the category Sh(X) of sheaves on X is equivalent to the localization W − 1PSh(X). In particular, for any presheaf F, there is a local isomorphism F → F GOOD ALGEBRAIC NUMBER THEORY BOOKS 27. Marcus's Number Fields is a good intro book, but it's not in LaTeX, so it looks ugly. Also doesn't do any local (p-adic) theory, so you should pair it with Gouvêa's excellent intro p-adic book and you have a great first course in algebraic number theory. MATHOVERFLOWQUESTIONSUNANSWERED MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up. Sign up to jointhis community
MATHOVERFLOW
Finding all proper divisors of a 3 z 3 + a 2 z 2 + a 1 z + 1 of the form x z + 1. nt.number-theory divisors-multiples. modified 29 mins ago David Jones 161. -1. votes. 0. answers. 61. views. FA.FUNCTIONAL ANALYSIS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
AT.ALGEBRAIC TOPOLOGY Let ( G, n) be a pair such that n is a natural number, G is a finite group which is abelian if n ≥ 1. It is well-known that π n ( K ( G, n)) = G and π i ( K ( G, n)) = 0 if i ≠ n. Also it is known that these spaces K ( G, n) play a very important role for cohomology. For any abelian group G, and any CW-complex X, the set [ X, K (HOMOLOGICAL ALGEBRA
Excercise 2.2.1 in Weibel ("An Introduction to Homological Algebra") states that an object P in the category of chain complexes over an abelian category is projective if and only it is a split exact complex of projectives. I was able to solve the only-if-part but I have touble with the if-part and would be glad if someone can give me some help.SHEAF THEORY
A map F → G of PSh(X) is said to be a local isomorphism if for every point x ∈ X, the induced map Fx → Gx on stalks is a bijection. Denote by W the class of local isomorphisms. Now the category Sh(X) of sheaves on X is equivalent to the localization W − 1PSh(X). In particular, for any presheaf F, there is a local isomorphism F → F AG.ALGEBRAIC GEOMETRY Special values of L-functions as periods. If M is a pure motive over Q, one cas define its L -function L(M, s) which conjecturaly is a meromorphic function over C with finitely many poles. For example, when M = Q is the trivial motive, L(Q, s) is the Riemann Zeta function ζ(s). There is a famous concjecture saying that all values of L(M, s)at
HOMOTOPY PULLBACK IN THE CATEGORY OF DG ALGEBRAS I was wondering if somebody could tell me the definition of homotopy pullback. Suppose $\def\C{{\cal C}}\C$ is a relative category, i.e., a category equipped with a subcategory, morphisms in which are known as weak equivalences.For example, take the category ofREFERENCE REQUEST
I am reading a textbook on PDE (Introduction to Elliptic and Parabolic Partial Differential Equations by Z. Wu, J. Yin and C. Wang, writtenin Chinese) where a
PR.PROBABILITY
I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis' 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading. MATHOVERFLOWQUESTIONSUNANSWERED MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up. Sign up to jointhis community
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Finding all proper divisors of a 3 z 3 + a 2 z 2 + a 1 z + 1 of the form x z + 1. nt.number-theory divisors-multiples. modified 29 mins ago David Jones 161. -1. votes. 0. answers. 61. views. FA.FUNCTIONAL ANALYSIS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
AT.ALGEBRAIC TOPOLOGY Let ( G, n) be a pair such that n is a natural number, G is a finite group which is abelian if n ≥ 1. It is well-known that π n ( K ( G, n)) = G and π i ( K ( G, n)) = 0 if i ≠ n. Also it is known that these spaces K ( G, n) play a very important role for cohomology. For any abelian group G, and any CW-complex X, the set [ X, K (HOMOLOGICAL ALGEBRA
Excercise 2.2.1 in Weibel ("An Introduction to Homological Algebra") states that an object P in the category of chain complexes over an abelian category is projective if and only it is a split exact complex of projectives. I was able to solve the only-if-part but I have touble with the if-part and would be glad if someone can give me some help.SHEAF THEORY
A map F → G of PSh(X) is said to be a local isomorphism if for every point x ∈ X, the induced map Fx → Gx on stalks is a bijection. Denote by W the class of local isomorphisms. Now the category Sh(X) of sheaves on X is equivalent to the localization W − 1PSh(X). In particular, for any presheaf F, there is a local isomorphism F → F AG.ALGEBRAIC GEOMETRY Special values of L-functions as periods. If M is a pure motive over Q, one cas define its L -function L(M, s) which conjecturaly is a meromorphic function over C with finitely many poles. For example, when M = Q is the trivial motive, L(Q, s) is the Riemann Zeta function ζ(s). There is a famous concjecture saying that all values of L(M, s)at
HOMOTOPY PULLBACK IN THE CATEGORY OF DG ALGEBRAS I was wondering if somebody could tell me the definition of homotopy pullback. Suppose $\def\C{{\cal C}}\C$ is a relative category, i.e., a category equipped with a subcategory, morphisms in which are known as weak equivalences.For example, take the category ofREFERENCE REQUEST
I am reading a textbook on PDE (Introduction to Elliptic and Parabolic Partial Differential Equations by Z. Wu, J. Yin and C. Wang, writtenin Chinese) where a
PR.PROBABILITY
I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis' 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading.NEWEST QUESTIONS
The number of solutions of 2 x p x + k = y 2. Let's consider the family of diophantine equations. 2 x p x + k = y 2. being p > 2 a prime and k a positive integer. An example is given by the equation. 2 x ⋅ 3 x + 97 = y 2. that presents, at least, nt.number-theory prime-numbers diophantine-equations.ASK A QUESTION
Ask a public question. Step 1: Draft your question. Step 2: Review your question. Title. Be specific and imagine you’re asking a question to another person. Similar questions. Body. Include all the information someone would need to answer your question. Thanks for contributing an answer to MathOverflow!NT.NUMBER THEORY
nt.number theory - L-function terminology - MathOverflow. 2. Let E / F be a quadratic extension of two number fields. Denote by f the conductor of E / F and let χ be the primitive Hecke Grossencharacter mod f associated to the non-trivial character of the abelian group G a l ( E / F) = Z / 2 Z.REFERENCE REQUEST
19 hours ago · Question: On balance, with theoretical advances in algorithmic information theory and Quantum Computation it appears that the remarkable effectiveness of mathematics is AT.ALGEBRAIC TOPOLOGY Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
HOW DO WE STUDY IWASAWA THEORY? The specific example that Iwasawa studied was the p -Sylow subgroup of the class group of K n = Q ( ζ p n). It's naturally a Z p -module as well as a G n = Gal ( K n / K 1) -module, but the group ring Z p isn't very nice; it's not a domain, for instance. If we instead look at the inverse limits of the p OPEN PROBLEMS WITH MONETARY REWARDS A. Bressan has advertised two monetary rewards of $500 each for solutions to problems on mixing flows and blocking problems. The first problem was unsolved as of Jan. 15, 2011, although progress in relevant directions is noted in the linked announcement. The second problem was announced on Jan. 19, 2011. Share. GOOD ALGEBRAIC NUMBER THEORY BOOKS 27. Marcus's Number Fields is a good intro book, but it's not in LaTeX, so it looks ugly. Also doesn't do any local (p-adic) theory, so you should pair it with Gouvêa's excellent intro p-adic book and you have a great first course in algebraic number theory. DG.DIFFERENTIAL GEOMETRY In this case, a classical theorem of Mostow (in 1950 for surfaces, in 2005 in general) says that for a compact homogeneous space M = G / H the Euler characteristics is non-negative. Mostow, G.D.: The extensibility of local Lie groups of transformations and groups onsurfaces. Ann.
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HOW DO WE STUDY IWASAWA THEORY? The specific example that Iwasawa studied was the p -Sylow subgroup of the class group of K n = Q ( ζ p n). It's naturally a Z p -module as well as a G n = Gal ( K n / K 1) -module, but the group ring Z p isn't very nice; it's not a domain, for instance. If we instead look at the inverse limits of the pHOMOLOGICAL ALGEBRA
Excercise 2.2.1 in Weibel ("An Introduction to Homological Algebra") states that an object P in the category of chain complexes over an abelian category is projective if and only it is a split exact complex of projectives. I was able to solve the only-if-part but I have touble with the if-part and would be glad if someone can give me some help.SHEAF THEORY
A map F → G of PSh(X) is said to be a local isomorphism if for every point x ∈ X, the induced map Fx → Gx on stalks is a bijection. Denote by W the class of local isomorphisms. Now the category Sh(X) of sheaves on X is equivalent to the localization W − 1PSh(X). In particular, for any presheaf F, there is a local isomorphism F → F TEACHING - HOW TO DRAW KNOTS WITH LATEX? - MATHOVERFLOW Update 2013-04-22: I've now uploaded a TikZ library to CTAN expressly for the purpose of drawing knots.It is already in MikTeX (according to CTAN), TeXLive might have to wait until TL2013 has been released. It is released as part of the spath3 library. Here's the link to CTAN.The hobby package also contains some useful code for drawing knots. For drawing braids, there's the braids package. AT.ALGEBRAIC TOPOLOGY Let ( G, n) be a pair such that n is a natural number, G is a finite group which is abelian if n ≥ 1. It is well-known that π n ( K ( G, n)) = G and π i ( K ( G, n)) = 0 if i ≠ n. Also it is known that these spaces K ( G, n) play a very important role for cohomology. For any abelian group G, and any CW-complex X, the set [ X, K (HO.HISTORY OVERVIEW
Edmund Landau's thesis was 13 pages long. I believe the shortest PhD thesis is of Burt Totaro "Milnor K-theory is the simplest part of algebraic K-theory", 12 pages. Milnor K-theory is the simplest part of algebraic K-theory, Ph.D. thesis, University of California, Berkeley, 1989; published as: K-Theory 6 (1992), 177-189 ( Portico archivedREFERENCE REQUEST
I am reading a textbook on PDE (Introduction to Elliptic and Parabolic Partial Differential Equations by Z. Wu, J. Yin and C. Wang, writtenin Chinese) where a
CO.COMBINATORICS
Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
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FA.FUNCTIONAL ANALYSIS Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
HOW DO WE STUDY IWASAWA THEORY? The specific example that Iwasawa studied was the p -Sylow subgroup of the class group of K n = Q ( ζ p n). It's naturally a Z p -module as well as a G n = Gal ( K n / K 1) -module, but the group ring Z p isn't very nice; it's not a domain, for instance. If we instead look at the inverse limits of the pHOMOLOGICAL ALGEBRA
Excercise 2.2.1 in Weibel ("An Introduction to Homological Algebra") states that an object P in the category of chain complexes over an abelian category is projective if and only it is a split exact complex of projectives. I was able to solve the only-if-part but I have touble with the if-part and would be glad if someone can give me some help.SHEAF THEORY
A map F → G of PSh(X) is said to be a local isomorphism if for every point x ∈ X, the induced map Fx → Gx on stalks is a bijection. Denote by W the class of local isomorphisms. Now the category Sh(X) of sheaves on X is equivalent to the localization W − 1PSh(X). In particular, for any presheaf F, there is a local isomorphism F → F TEACHING - HOW TO DRAW KNOTS WITH LATEX? - MATHOVERFLOW Update 2013-04-22: I've now uploaded a TikZ library to CTAN expressly for the purpose of drawing knots.It is already in MikTeX (according to CTAN), TeXLive might have to wait until TL2013 has been released. It is released as part of the spath3 library. Here's the link to CTAN.The hobby package also contains some useful code for drawing knots. For drawing braids, there's the braids package. AT.ALGEBRAIC TOPOLOGY Let ( G, n) be a pair such that n is a natural number, G is a finite group which is abelian if n ≥ 1. It is well-known that π n ( K ( G, n)) = G and π i ( K ( G, n)) = 0 if i ≠ n. Also it is known that these spaces K ( G, n) play a very important role for cohomology. For any abelian group G, and any CW-complex X, the set [ X, K (HO.HISTORY OVERVIEW
Edmund Landau's thesis was 13 pages long. I believe the shortest PhD thesis is of Burt Totaro "Milnor K-theory is the simplest part of algebraic K-theory", 12 pages. Milnor K-theory is the simplest part of algebraic K-theory, Ph.D. thesis, University of California, Berkeley, 1989; published as: K-Theory 6 (1992), 177-189 ( Portico archivedREFERENCE REQUEST
I am reading a textbook on PDE (Introduction to Elliptic and Parabolic Partial Differential Equations by Z. Wu, J. Yin and C. Wang, writtenin Chinese) where a
CO.COMBINATORICS
Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit StackExchange
NEWEST QUESTIONS
2D-metric to diagonal form with determinant 1. I wonder whether it is always possible to bring a 2D Riemannian metric to a diagonal form with determinant one by changing the coordinates, i.e. for the line element $$ ds^2 = A (x,y)\, dx^2 + B (x, riemannian-geometry. askedyesterday. Nikodem.
FIELDS - VALUATION TOPOLOGY VS MODIFIED - MATHOVERFLOW Elsevier, 1987, by Alling, Norman L., the valuation topology on K is defined as the one with base { B ( x 0, > g): g ∈ G, x 0 ∈ K } where. B ( x 0, > g) = { x ∈ K: v ( x − x 0) > g }. He shows that K equipped with this topology is a Hausdorff topological field, and if K is an ordered field then the order topology coincides with the REFERENCE BOOK FOR COMMUTATIVE ALGEBRA Another one is being written. Combinatorial commutative algebra: Miller-Sturmfels. Geometry of syzygies: Eisenbud, shorter but free version here. Homological conjectures: Hochster, Roberts (more connections to intersection theory), Hochster notes. Integral closures: Huneke-Swanson, which is available free at the link. OPEN PROBLEMS WITH MONETARY REWARDS A. Bressan has advertised two monetary rewards of $500 each for solutions to problems on mixing flows and blocking problems. The first problem was unsolved as of Jan. 15, 2011, although progress in relevant directions is noted in the linked announcement. The second problem was announced on Jan. 19, 2011. Share.DERIVED CATEGORIES
2. As I understand the construction of the determinant of a perfect complex, this definition is quite straightforward, following from the fact that in a short exact sequence, say. 0 → S → E → Q → 0. defining the determinant of the sequence to be the alternating tensoris
AC.COMMUTATIVE ALGEBRA R is a field in its own right with the standard operations and R^2 can be made into a field by introducing the product (a,b)* (c,d) = (ac-bd,ad+bc) i.e. the product ofREFERENCE REQUEST
Another standard reference is the book of Banyaga and Hurtubise. Banyaga, Augustin; Hurtubise, David Lectures on Morse homology. Kluwer Texts in the Mathematical Sciences, 29. Kluwer Academic Publishers Group, Dordrecht, 2004. A book that is tough to read, but is a gateway to Floer theory is Schwarz' book. AG.ALGEBRAIC GEOMETRY Here's probably the simplest manifestation of the field-with-one-element phenomenon. Define a projective n -space of order q to be a collection of points, lines, planes, etc. satisfying the usual incidence relations with the additional condition that every line has q + 1 pointsSOFT QUESTION
Publishing a Simple Paper as an Undergraduate. First off I apologize if this question does not belong here, I would be happy to hear about any better locations to post this on. I am a (first year) undergraduate mathematics student, and I recently discovered some interesting properties hidden in certain families of sequences. IS THERE A MANIFOLD WITH FUNDAMENTAL GROUP $\MATHBB{Q The answer to both questions is "Yes". As Fernando Muro mentioned, any countable group is the fundamental group of a manifold that can be embedded in R 5. There is an open subset of R 3 with fundamental group Q, the complement of a particular solenoid. Let C 1 be the complement of an unknotted solid torus. π 1 ( C 1) = x 1 . STACK EXCHANGE NETWORK Stack Exchange network consists of 176 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and buildtheir careers.
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