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

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4
votes
0answers
38 views

The definition of < in Robinson's Q

I recently had to explain how the basic axioms in Simpson's Subsystems of Second Order Arithmetic were interpretable in Robinson's Q. Most of the axioms are actually the same, except that Simpson ...
0
votes
0answers
128 views

Grothendieck's letter to serre

Is it the letter dated in 27/08/1965 of Grothendieck where he presents to Serre the Standard conjectures on algebraic cycles?
1
vote
0answers
47 views

A topological criterion for connectedness of a semi-ample divisor

I have a half page long proof of the following statement, and I would like to know if this is (a corollary of) a well known statement. Maybe there is a reference or a three lines proof? Statement. ...
1
vote
1answer
105 views

Localization of symmetric monoidal category

Let $\mathcal M$ be a symmetric monoidal category, $S\subset \mathcal M$ a collection of objects and morphisms. I would like to construct the localization $\mathcal M \mathop{\longrightarrow}^T ...
2
votes
3answers
368 views

Reference request: SGA7

I want to read SGA7. Without considering the others SGA and EGA, Which are the textbooks for monodromy theory?
2
votes
1answer
70 views

References for the Keisler Order

Are there any good/modern references on the Keisler order. I have been reading Keisler's original paper, "Ultraproducts which are not Saturated", which introduces the order. However it is somewhat ...
3
votes
1answer
132 views

Ergodic theory reference for converging sequences of matrices

I have been told that the following is a well known theorem in ergodic theory & have been given the book by Furstenberg as a reference. However, I cannot find such a statement in it. Would anyone ...
2
votes
0answers
28 views

Generators for lattice polytopes

Let $V$ be a finite set of integral vectors in $\mathbb{R}_n$. Consider the real (positive) convex cone $\mathbb{R}^+V$ spanned by $V$. We can assume that all vectors in $V$ are extremal in ...
5
votes
1answer
232 views

Serious introduction to the Langlands program for nonspecialist

I recently became interested in the Langlands program and hope to learn more. For context, I am an analytic number theorist but have some light background in algebraic number theory and modular ...
5
votes
1answer
224 views

Detection of stable homotopy by K-theory spectra

This is primarily a reference request. Does anyone know of any writing about algebraic K-theory spectra picking up elements in the stable homotopy groups of spheres in their Hurewicz image coming from ...
-2
votes
0answers
65 views

Any other operators that may convert agebraic function into transcendental ones [on hold]

As we know,integral may convert or map a rational function or algebraic function into transcendental one,are there any other operators that may convert a rational function or algebraic function into ...
7
votes
3answers
501 views

nth term in the Baker-Campbell-Hausdorff formula

I am trying to prove a result for which I need the nth term of the Baker-Campbell-Hausdorff formula. I came at this particular result (which is not of significance for the question, but mentioning for ...
1
vote
0answers
84 views

References for crystal bases and Demazure modules in representation theory

I was wondering what are some standard general references/books/survey articles about: (1) crystal bases, and string parameterizations and (2) Demazure modules, and Schubert varieties (containing ...
2
votes
0answers
114 views

Noncommutative HKR theorem

What is the analog of HKR theorem in the noncommutative world? Recall that the well-known theorem by Hochschild-Kostant-Rosenberg says that for a smooth commutative algebra $A$ of finite type ...
1
vote
2answers
92 views

Asymptotics and error terms for an arithmetic function built upon $\omega$ and $\Omega$ functions

For any real number $x$, let's define $Om_{k}(x)$ as the number of positive integers $m$ below $x$ such that $\Omega(m)-\omega(m)=k$, where $\omega(n)$ is the number of distinct primes dividing $n$, ...
-2
votes
0answers
46 views

Di Perna-Lions theory for transport equation [on hold]

Does someone know if some notes on the topic mentioned in the title are available online? I'm reading the paper "Ordinary differential equations, transport theory and Sobolev spaces" by Di Perna and ...
2
votes
0answers
42 views

Uniformization/measurable selection theorems

Let $X,Y$ be measurable spaces and $F\subseteq X\times Y$. We say that $f:X\to Y$ is a uniformization map for $F$ if $(x,f(x))\in F$ for each $x\in \pi_X(F)$ where $\pi_X$ is the left projection map. ...
2
votes
2answers
196 views

Basic questions on the Hilbert scheme/ Douady space

Let $X$ be a complex projective scheme (resp. complex analytic space). The Hilbert scheme (resp. Douady space) parameterizes closed subschemes (resp. complex analytic subspaces) of $X$. More ...
0
votes
1answer
236 views

a book comparable to Development of mathematics in the 19th century by F.Klein? [on hold]

This book is apparently very interesting according to Vladimir Arnold. I couldn't get my hand on a copy yet, therefore I would to ask you for any reference similar to it, and also can you post ...
9
votes
3answers
1k views

Weil's Riemann Hypothesis for dummies?

Weil's Riemann Hypothesis is a deep result that I don't fully understand, but it has understandable corollaries which interest me. For example: (a) For any projective curve $X$ satisfying certain ...
1
vote
0answers
45 views

polynomial 0,1 integer programming

IS there a mathematical optimization branch that explicitly tries to optimize this (type) problem? $$\eqalign{ & \min \cr & \sum\limits_{i = 1}^N {(J*s[i] + {J_1}*s[i]*s[i + 1] + ...
2
votes
1answer
174 views

Tools for Removing Radicals from Equations

I am currently doing some investigations on Sylvester's 4 Point Problem Probability of 4 Points being in Convex Configuration and repeatedly face the problem of solving equations between sums of ...
6
votes
1answer
278 views

Complex geometry text/research introduction for the analyst

To give some background, I am mainly an analyst trained in harmonic/functional and do work on geometric pde's and spectral multipliers. Of late, I am trying to learn more about (research level) ...
1
vote
0answers
28 views

Jumps of jump diffusions

Let $W$ be a Brownian motion and $N$ a Poisson random measure defined on $\mathbb R_+ \times \mathbb R_0^n$ ($\mathbb R_0^n:=\mathbb R^n-\{0\}$) with compensator $\tilde N(dt,dz):= N(dt,dz) - dt ...
1
vote
0answers
82 views

How does one show that slope stability of a vector bundle is an open condition with respect to the polarisation?

I would like a source for the following result, which I expect to be true (probably well known): Let $X$ be a complex projective variety, $L$ an ample line bundle and $E$ a slope stable vector bundle ...
0
votes
3answers
169 views

Specific Reference? Noncommutative topology and C^* algebras [closed]

I stumbled across this "dictionary for noncommutative topology" http://planetmath.org/noncommutativetopology and I would be very interested in learning more on the subject, particularly I'd like to ...
2
votes
0answers
51 views

Reference for MacMahon on Overpartitions

In the literature on overpartitions Percy A. MacMahon is usally cited as the genesis of the theory. Often the reference is to his 1916 textbook -- but, having recently checked this out of my school's ...
1
vote
2answers
91 views

Does the Teichmüller space of the pair of pants admit a continuous global section?

Let $P$ be a pair of pants, $H(P)$ be the space of smooth hyperbolic Riemannian metrics with geodesic boundary on $P$, and $T(P)$ be the Teichmüller space of $P$ (quotient of $H(P)$ under smooth ...
0
votes
0answers
164 views

NonCommutative analog of the Poincare Bendixson theorem [closed]

The classical Poincare Bendixson theorem says: If $X$ is a vector field on $\mathbb{R}^{2}$ or $S^{2}$ and $K$ is a compact set which is invariant under the flow generated by $X$. Then $K$ contains ...
2
votes
0answers
50 views

Properties of the induced map between inertia stacks

Let $\mathcal X$ and $\mathcal Y$ be (separated) Deligne-Mumford stacks. A morphism of stacks $f:\mathcal X \to \mathcal Y$ induces a morphism between inertia stacks $\tilde f:I\mathcal X \to ...
3
votes
1answer
134 views

Flat family with special fiber $\mathbb{C}\mathbb{P}^1$

Let $C=Spec \mathbb{C}[t]/(t^{n+1})$. Let $X$ be an algebraic (or complex analytic) scheme, flat over $C$ with the structure morphism $f\colon X\to C$. Assume that the special fiber is isomorphic to ...
2
votes
2answers
194 views

irreducible polynomials on the polynomial sequence

I suspect this problem is very famous and it must be studied very well. But I searched in Google and I did not find good reference. I will appreciate any answer and reference for any contribution ...
2
votes
0answers
65 views

Countable model theory for $\omega$-stable theories?

This is a bit of a fishing expedition, because I'm not sure what I'm looking for. Very vaguely stated, here's the driving question: What conditions on an $\omega$-stable theory make the class of ...
1
vote
1answer
276 views

When flatness of a morphism implies smoothness?

EDIT: Let $f\colon X\to C$ be a flat proper morphism of complex algebraic (or analytic) varieties. Assume the special fiber over a point $p\in C$ is smooth. Is it true that there exists a ...
2
votes
1answer
55 views

Does the category PCM (partial commutative monoids) have a closed symmetric monoidal product?

A partial commutative monoid (PCM) is, roughly speaking, a set with a partially defined binary operation that is as associative as it can be (given that not all products are defined) and commutative. ...
3
votes
0answers
99 views

Parshin's buildings for higher local fields

What is the status of the theory of buildings for higher local fields? I know that there are some papers of Parshin, in which he describes some examples, like $PGL_2$ and $PGL_3$ over ...
2
votes
0answers
170 views

Some explanation about Dynin's formalism

I have seen this claim on the Wikipedia page for the Yang-Mills Millenium problem by Alexander Dynin. He is a mathematician working at the Department of Mathematics of Ohio State University and so, I ...
0
votes
0answers
280 views

Conjectures on fractions where each digit appears once in numerator and denominator

This is a highly redacted version of a question that was asked before. Please see Criteria of considering relevance of the question to the domain of research topics for details. Some numerical ...
2
votes
0answers
130 views

On groups satisfying a law

We say that a group $G$ satisfies a law if there exists a (nontrivial) word $w \in \mathbb{F}_n$ such that $w(g_1,\dots,g_n)=1$ for every $g_1,\dots, g_n \in G$. For example, any abelian group ...
0
votes
1answer
186 views

Where can I find the classification of groups of order 16p? [closed]

I need to classify the groups of order $16p$ by their generators and relations between the generators. Can I find this classification anywhere?
5
votes
2answers
156 views

What is known about tiling a rectangle in an irreducible way by smaller rectangles?

Given two naturals $s<t$. Is there always a square (or at least a bigger rectangle) that can be tiled with $s\times t$ rectangles in an irreducible way (i.e. any grid line splitting it cuts at ...
4
votes
2answers
151 views

Forcing $\neg AC$

Sorry if this sounds like a silly reference request, but I wasn't able to track down any. I'm looking for proof, via forcing, that axiom of choice can fail in a model of $ZF$. All of papers I found ...
0
votes
0answers
31 views

reading request on linear elliptic systems of pdes, strong solutions

Does anyone have some references where I could find results on strong solutions to linear elliptic systems of pdes ? Regards
2
votes
0answers
69 views

singularities preserved by integral closure

Let $X$ be an affine variety. Let $A$ be the coordinate ring of $X$ and let $K$ be the fraction field of $A$. Given a Galois extension $K\subset L$, let $B$ be the integral closure of $A$ in $L$. Let ...
5
votes
0answers
105 views

A Property of Generalized Equivariant Cohomology

Let $G_i$ be a compact Lie group, $i=1,2$, and let $E_{G_i}^*$ be a $\mathbb{Z}$-graded complex-oriented $G_i$-equivariant generalized cohomology theory with commutative products. Let $X_i$ be a ...
2
votes
0answers
36 views

Probability of hitting a Borel set by transient Brownian motion ($d\geq 3$)

I am looking for references/progress made in estimating the hitting probability for Borel sets. For spheres we have $P_{x}(T_{B_{r}(0)}<\infty)=(\frac{|r|}{|x|})^{d-2}$, where $x=B_{0}$ for ...
0
votes
1answer
191 views

Articles about Weil cohomology theory by Grothendieck and Artin

In "The Standard Conjectures" Kleiman says that the following properties of Weil cohomology theory were proved in 1963 for étale cohomology by Artin and Grothendieck, except for the last one that it ...
5
votes
0answers
74 views

$L^p$ regularity for wave equations with coercive boundary conditions

Suppose we have the wave type equation $$\partial^2_tu - L u = 0$$ on a compact manifold with boundary, where $L$ is a second order strongly elliptic operator with coercive boundary conditions (not ...
2
votes
1answer
251 views

Is there any publication of “Beilinson’s dream” on motivic (complexes of) sheaves?

In "Standard conjectures of algebraic cycles" nLab says: "... They were also followed by “Beilinson’s dream” on motivic (complexes of) sheaves which comprise so called standard conjectures of ...
3
votes
0answers
66 views

Variational Principle for a System of Differential Equations

I am studying a differential operator of the form $$ L\left(\begin{array}{c} u \\ v \end{array}\right) = -\Delta \left(\begin{array}{c} u \\ v \end{array}\right) + V(x)\left(\begin{array}{c} u \\ v ...