# Questions tagged [reference-request]

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

9,746
questions

**18**

votes

**7**answers

3k views

### English reference for a result of Kronecker?

Kronecker's paper Zwei Sätze über Gleichungen mit ganzzahligen Coefficienten apparently proves the following result that I'd like to reference:
Let $f$ be a monic polynomial with integer ...

**11**

votes

**2**answers

556 views

### Reference request: The stable Kronecker ring is isomorphic to the ring of symmetric polynomials

Background
For $\lambda$ any partition and $n$ a positive integer, write $\lambda[n]$ for the sequence $(n - |\lambda|, \lambda_1, \lambda_2, \ldots, \lambda_r)$. For $n$ large enough, this is a ...

**7**

votes

**3**answers

818 views

### References for theorem about unipotent algebraic groups in char=0?

There is a textbook theorem that the categories of unipotent algebraic groups and nilpotent finite-dimensional Lie algebras are equivalent in characteristic zero. Indeed, the exponential map is an ...

**10**

votes

**9**answers

2k views

### Comprehensive reference for synthetic euclidean geometry

Euclidean geometry is a special case of the theory of Hilbert spaces; but in order to convince small children of basic facts, e.g. that the line segments from each of the vertices of a triangle to the ...

**163**

votes

**48**answers

54k views

### Ways to prove the fundamental theorem of algebra

This seems to be a favorite question everywhere, including Princeton quals. How many ways are there?
Please give a new way in each answer, and if possible give reference. I start by giving two:
...

**25**

votes

**10**answers

9k views

### Uniformization theorem for Riemann surfaces

How does one prove that every simply connected Riemann surface is conformally equivalent to the open unit disk, the complex plane, or the Riemann sphere, and these are not conformally equivalent to ...

**19**

votes

**9**answers

10k views

### Teichmuller Theory introduction

What is a good introduction to Teichmuller theory, mapping class groups etc., and relation to moduli space of curves or Riemann surfaces?

**12**

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

2k 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/...

**18**

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

6k 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 ...

**28**

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 ...

**16**

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 (...

**35**

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

**6**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

400 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

269 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 ...

**326**

votes

**78**answers

148k 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 ...

**18**

votes

**15**answers

15k 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 ...

**11**

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

534 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

970 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 ...

**19**

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

848 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 ...

**11**

votes

**6**answers

10k 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

570 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 $\...

**36**

votes

**12**answers

9k 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

564 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 ...

**56**

votes

**16**answers

11k 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

268 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

1k 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

578 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 ...

**54**

votes

**14**answers

17k 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 ...