# Questions tagged [reference-request]

This tag is used if a reference is needed in a paper or textbook on a specific result.

11,191
questions

**15**

votes

**6**answers

2k views

### “Every scheme as a sheaf” references?

I have sometimes hard time reading papers that are written in the language of schemes being replaced by the functors they represent (I have especially homotopy scheme theory in mind).
I think the ...

**15**

votes

**5**answers

3k views

### Reference for this theorem in representation theory?

Let $G$ be a finite group and $\chi$ be an irreducible character of
$G$ (characteristic zero algebraically closed base field). If $H$ is
the kernel of $\chi$ then the irreducible representations of $G/...

**19**

votes

**5**answers

1k views

### Equivalence of ordered and unordered cech cohomology.

Given a topological space X and a finite cover X = $\cup X_i$, one can define Cech cohomology of a sheaf of abelian groups F with respect to the cover $\{X_i\}$ in two different ways:
(Ordered): ...

**14**

votes

**4**answers

7k views

### Who invented the gamma function?

Who was the first person who solved the problem of extending the factorial to non-integer arguments?
Detlef Gronau writes [1]: "As a matter of fact, it was Daniel Bernoulli who gave in 1729 the ...

**29**

votes

**3**answers

4k views

### Matrix factorizations and physics

I have heard during some seminar talks that there are applications of the theory of
matrix factorizations in string theory. A quick search shows mostly papers written by physicists. Are there any ...

**17**

votes

**4**answers

2k views

### Characteristic classes in generalized cohomology theories?

Hello,
'ordinary' Stiefel-Whitney classes are elements of the singular cohomology ring and are constructed using the Thom isomorphism and Steenrod squares. So I think they should exist for any (...

**36**

votes

**4**answers

3k views

### How far is Lindelöf from compactness?

A while ago I heard of a nice characterization of compactness but I have never seen a written source of it, so I'm starting to doubt it. I'm looking for a reference, or counterexample, for the ...

**11**

votes

**3**answers

3k views

### References for Donaldson-Thomas theory and Pandharipande-Thomas theory?

I'm looking for good introductory references for Donaldson-Thomas theory and Pandharipande-Thomas theory. I know a bit about Gromov-Witten theory, but almost nothing about Donaldson-Thomas and ...

**22**

votes

**7**answers

5k views

### What are some good resources for mathematical translation?

I am currently in the process of translating a lecture on the étale topology by John Hubbard from French into English (and from transparencies into Beamer). For the most part, the translation is ...

**5**

votes

**1**answer

431 views

### Request for reference: Banach-type spaces as algebraic theories.

Sparked by Yemon Choi's answer to Is the category of Banach spaces with contractions an algebraic theory? I've just spent a merry time reading and doing a bit of reference chasing. Imagine my delight ...

**5**

votes

**2**answers

274 views

### Truncated exact sequence of homotopy groups

This is a question about a name of a very useful lemma,
that permits one in particular to show that smooth birational complex projective
varieties have isomorphic fundamental groups.
If this lemma ...

**350**

votes

**79**answers

159k views

### Proofs without words

Can you give examples of proofs without words? In particular, can you give examples of proofs without words for non-trivial results?
(One could ask if this is of interest to mathematicians, and I ...

**8**

votes

**1**answer

1k views

### Elementary questions in arithmetic geometry

In many theories there is a rough divide between elementary problems that can be solved with "one's hands", and "deep results that require powerful tools". For example, I am told that Hodge theory is ...

**3**

votes

**5**answers

2k views

### Martingales and Betting Strategies

Does anyone know of a good introduction to the theory of martingales and betting strategies from the point of view of statistics and/or probability theory? I'm looking for something basic, with lots ...

**22**

votes

**15**answers

16k views

### Learning Topology

EDIT (Harry): Since this question in its original form was poorly stated (asked about topology rather than graph theory), but we have a list of Topology books in the answers, I guess you should go ...

**12**

votes

**6**answers

2k views

### Reference for Learning Global Class Field Theory Using the Original Analytic Proofs?

Hi Everyone!
I'm wondering if anyone knows of a reference for learning global class field theory using the original analytic proofs developed in the 1920s and 1930s. Almost every book I can find ...

**12**

votes

**0**answers

538 views

### References for a certain generalization of Hochschild cohomology?

Let $C$ be an algebra. Let $E = C^{\otimes 2n}$ be the tensor product (over the ground field) of $2n$ copies of $C$. [EDIT: Or better, $E = C\otimes C^{op}\otimes C\otimes C^{op}\cdots\otimes C \...

**3**

votes

**4**answers

994 views

### Examples of divisors on an analytical manifold

I am trying to understand divisors reading through Griffith and Harris but it is difficult to come up with any particular interesting example. I have browsed through Hartshone's book but everything is ...

**21**

votes

**3**answers

3k views

### Twin Prime Conjecture Reference

I'm looking for a reference which has the first statement of the twin prime conjecture. According to wikipedia, nova, and several other quasi-reputable resources it is Euclid who first stated it, but ...

**18**

votes

**0**answers

1k views

### Two conjectures by Gabber on Brauer and Picard groups

In a paper I need to make reference to 2 conjectures by Gabber
(see Conjectures 2 and 3, page 1975)
http://www.mfo.de/programme/schedule/2004/32/OWR_2004_37.pdf
1) Let $R$ be a strictly henselian ...

**10**

votes

**0**answers

1k views

### Complexes of representations with complementary central charges

This is another question asking for references. There is an important phenomenon of correspondence between (complexes of) representations of infinite-dimensional Lie algebras with the complementary ...

**9**

votes

**5**answers

950 views

### References/literature for pushouts in category of commutative monoids? [ed. - amalgams]

This is more of a request for pointers to relevant literature than a question per se. I am, erm, looking at a paper which uses a kind of iterated pushout construction to obtain a commutative monoid ...

**12**

votes

**6**answers

11k views

### What books should I read before beginning Masaki Kashiwara's “Sheaves on Manifolds”

I am a beginner trying to learn about sheaves. I am trying to read Masaki Kashiwara's book "Sheaves on Manifolds", but I find it is not easy for me to understand.
What other books should I read first,...

**14**

votes

**3**answers

3k views

### References for equivariant K-theory

I want a good introduction to localization in equivariant $K$-theory. This introduction can be simple in several ways:
I only care about torus actions.
I only care about $K^0$.
I only care about very ...

**6**

votes

**7**answers

1k views

### CLT for stationary sequences with infinte variance

There is a well-known central limit theorem for as a stationary sequences.
If $( X_n )_n$ is a sationary sequence and $E X_n=0$ then under suitable mixing conditions the sequence $S_n := n^{-1/2}\...

**8**

votes

**1**answer

581 views

### Composite Residues with Determinant Denominators

I am looking for a good reference on composite residues of multi-variable contour integrals (something better and more explicit than Griffiths and Harris or Tsikh). This means I want to evaluate $\...

**41**

votes

**13**answers

10k views

### Introductory text on geometric group theory?

Can someone indicate me a good introductory text on geometric group theory?

**7**

votes

**7**answers

1k views

### A few questions on model theory, especially model theory of rings

I have never really read anything proper about model theory, so I have a few questions:
Someone told me that a school of logicians managed to give a very short proof of Falting's Theorem using model ...

**2**

votes

**3**answers

586 views

### Variant of binomial coefficients

I've recently come across a variant of the binomial polynomials, and I'm curious if anyone has seen these before. If so, I'd love a reference, a name, etc.
First recall the following. If z is a ...

**4**

votes

**3**answers

1k views

### Modular forms reference

If f is a weight 2 newform on $\Gamma_1(N)$ then there exists an abelian variety Af whose endomorphism algebra is isomorphic to the field generated by the coefficients of f.
I've seen this proven in ...

**18**

votes

**3**answers

1k views

### Elementary $\mathrm{Ext}^1$ intuition

$\DeclareMathOperator{\Hom}{\operatorname{Hom}}\DeclareMathOperator{\Ext}{\operatorname{Ext}}$I am wondering what sort of basic basic intuitive meaning $\Ext^1(M,N)$ has.
As a base case: if $M$ and $N$...

**61**

votes

**16**answers

13k views

### Good introductory references on algebraic stacks?

Are there any good introductory texts on algebraic stacks?
I have found some readable half-finsished texts on the net, but the authors always seem to give up before they are finished. I have also ...

**16**

votes

**1**answer

1k views

### Hopf Algebra Reference

I was talking this morning to a colleague who thinks about combinatorial Hopf algebras. He mentioned several rings, which are of interest in combinatorics, for which he didn't know whether a Hopf ...

**6**

votes

**1**answer

269 views

### Can you construct a mapping space from local data? (looking for reference)

I'd to know if/where there is a reference for the following construction.
Let C_*(maps(M, T)) denote the singular chains on the space of continuous maps from an n-...

**8**

votes

**6**answers

1k views

### References for Lie superalgebras

Does anybody know good references to learn about Lie superalgebras? I started with Howe's "Remarks on classical invariant theory", which contains a study of osp(m,2n), and now I am reading Kac's '77 ...

**8**

votes

**4**answers

1k views

### cohomology of moduli spaces

Does anyone know if there's any reference on the $\ell$-adic cohomology of some simple moduli spaces/Shimura varieties, like Siegel moduli varieties $A_{g,N}$ of genus $g$ and level $N,$ for small $g$ ...

**10**

votes

**4**answers

2k views

### References for syntomic cohomology

Could anyone point to good readable references for learning about syntomic cohomology?

**11**

votes

**1**answer

2k views

### Reference for the `standard' Tate curve argument.

I'd like a reference (e.g. something published somewhere that I can cite in a paper) for the proof of the following:
Let $E$ be an elliptic curve over $\mathbb Q$ with minimal discriminant $\Delta$...

**6**

votes

**3**answers

664 views

### Generic Noether Normalisation

Suppose that $M$ is a finitely generated module over $A=k[X_1,\ldots,X_n]$ of Krull dimension $m$ with $k$ an infinite field. Then one version of Noether normalisation says there is an $m$-dimensional ...

**15**

votes

**10**answers

3k views

### References for homotopy colimit

(1) What are some good references for homotopy colimits?
(2) Where can I find a reference for the following concrete construction of a homotopy colimit? Start with a partial ordering, which I will ...

**56**

votes

**14**answers

19k views

### A reading list for topological quantum field theory?

Can you suggest a reading list, or at least a few papers that you think would be useful, for a beginner in topological quantum field theory? I know what the curvature of a connection is, know basic ...