# Questions tagged [reference-request]

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

9,216 questions
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### Are there universe-indexed spectra over simplicial sets?

In "Rings, Modules, and Algebras in Stable Homotopy Theory" Elmendorf, Kriz, Mandell and May introduce a notation of spectra indexed over an universe $\mathcal{U}$ as a collection of pointed ...
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### References for logarithmic geometry

Hi everyone, I'm looking for a systematical introduction to (or treatment of) logarithmic structures on schemes. I am reading Kato's article ("Logarithmic structures of Fontaine-Illusie") at the ...
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### cardinal equivalence: for each boolean formula, |quantifications| = |assignments|. [closed]

Cardinal Equivalence Theorem For each boolean formula, |quantifications| = |assignments|. The set of valid quantifications has some cardinality, call that |Q(B)...
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### Non-commutative versions of X/G

Let $X$ be a Riemannian manifold and let $G$ be a (at most countable, if that matters) discrete group acting properly and by isometries on $X$. Let $\mathcal{O}$ be the sheaf of analytic functions on ...
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### Introductory text for the non-arithmetic moduli of elliptic curves

I'm looking for an introduction to the non-arithmetic aspects of the moduli of elliptic curves. I'd particularly like one that discusses the $H^1$ local system on the moduli space (whether it's $Y(1)$ ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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: ...
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### 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 ...
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### 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?
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### “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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...