# Questions tagged [reference-request]

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

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### Did Grothendieck-Serre write about toric varieties?

I'm curious if Grothendieck or Serre wrote anything about toric varieties? Were they aware of the notion? I would much appreciate any references.

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### The cover of the motivic sphere spectrum

Let $\mathbb{1}$ be the motivic sphere spectrum over an algebraically closed field $k$. Consider the $n-1$-cover of $\mathbb{1}$ in the Voevodsky′s slice tower $f_{n}(\mathbb{1})\to \mathbb{1}$.
My ...

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### Reference request: Gauge theory

What are some good introductory texts to gauge theory? I have some basic differential geometry knowledge, but I don’t know any algebraic geometry.
Also, as a side question, what intuitively is a ...

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### Reference Request: Total Variation Between Dependent and Independent Bernoulli Processes

Let $X$ be a random variable taking values in $\{0,1\}^n$ with the following distribution. For each coordinate $i$, we have $p_i = P(X_i = 1) = c/\sqrt n$, where $c$ is a (very small) constant. ...

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### Non-trivial foliation (excluding the Reeb foliation)

Let $M$ be a closed oriented manifold, an oriented foliation $F$ is said non-trivial, if $F$ is not fibration of $M$, i.e. there does not exist a closed manifold $B$, such that $M\overset{F}{\to} B$.
...

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### Iterated free infinite loop spaces

Let $Q$ denote $\Omega^\infty\circ \Sigma^\infty$ the free infinite loop space functor. Given some space $X$, we see that $QX$ carries all the stable homotopy information about $X$. Naturally I wanted ...

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### An easier reference than “On the Functional Equations Satisfied by Eisenstein Series”?

I'd like to learn about Eisenstein series so I started reading "On the Functional Equations Satisfied by Eisenstein Series"by Langlands.
http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/pdf/...

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### Recognizing a restriction from $SL_2(\mathbb{C})$ to $SL_2(\mathbb{Z})$

I am aware that classifying all $SL_2(\mathbb{Z})$ representations is more or less completely intractable, but I was wondering what is known about the following simpler question: How do I recognize ...

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### Is this line of thought (using linear algebra to get number theoretic results) already being pursued in the literature?

Let $Log(n) = \sum_{i=1}^r \alpha_i \cdot e_i$, where $n = \prod_{i=1}^r p_i^{\alpha_i}$ and $p_i$ is the $i$-th prime, $\alpha_i \ge 0$, $e_i$ is the $i$-th standard basis vector. For example $6 = 2\...

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### Reference request: $n$-edge-coloring bipartite graph $K_{n,n}$ such that monochromatic parts are isomorphic

I am finding references for the following problem:
We call a $n\times n$ 0-1 matrix permutation if there are exactly one $1$ in each row/column.
Suppose $A$ is a 0-1 matrix of size $n\times n$ in ...

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157 views

### Do analytic functionals form a cosheaf?

Let $X$ be a complex-analytic manifold.
Consider the sheaf of holomorphic functions $\mathcal{O}_X$ as a sheaf with values in the category of locally convex vector spaces. For $U\subseteq X$ open, we ...

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### Lambek calculus, linear logic, and linear algebra

In his 1958 paper, The Mathematics of Sentence Structure, Joachim Lambek introduced the Lambek calculus. In modern terms, it could be understood as a syntax for biclosed
monoidal categories, and he ...

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45 views

### Is there a three valued logic whose game semantics corresponds to potentially infinite games?

Consider game trees with the following properties:
Each node in the tree is one of the following:
Verifier Choice: Has one or more children
Falsifier Choice: Has one or more children
No Choice: Has ...

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26 views

### Bound for roots of a polynomial with coefficients in a non-Archimedean valued field

Is there any bound for the valuation of the roots of a given polynomial with coefficients in an algebraically closed non-Archimedean valued field?
Any reference or insight would be appreciated.

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### Heights for rational points via Neron models

I only just started reading about heights in arithmetic geometry, so forgive me if this question is naive.
Suppose $E$ is an elliptic curve over a number field $K$ with ring of integers $R$ and let $\...