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

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4
votes
2answers
125 views

Dimension of the nilpotent centralizer of a nilpotent matrix

Fix a natural number $n$ and an algebraically closed field $k$. Let $\mathfrak{g}=\mathfrak{gl}_n(k)$. For any partition of $n$, $\lambda=(\lambda_1,\ldots,\lambda_r)$, let $A_{\lambda}$ be the ...
1
vote
0answers
153 views

Smoothness of eigenfunctions of integral equation

Can you provide a proof or a reference, to study from, for the following problem: Assume $\Gamma$ is a real analytic closed rectifiable curve in the plane, $ds$ is the arc-length and kernel ...
4
votes
0answers
79 views

Relation between fundamental theorem of Ehrenfeucht-Fraisse games and notions of bisimulation and simulation

Vijay D alluded to the relation between the fundamental theorem of Ehrenfeucht-Fraisse games and notions of bisimulation and simulation in response to the whats-a-magical-theorem-in-logic question. ...
4
votes
2answers
249 views

What's an initial object in a poset-enriched category?

I have a functor $F:C \to D$ between poset-enriched categories, and I'd like to show that the induced map on classifying spaces is a homotopy-equivalence. To this end, I am trying to establish the ...
3
votes
1answer
47 views

Random weighted selection without replacement

I am using the following procedure to select $m$ different numbers $\{i_1,\ldots,i_m\}$ from the set $\Omega = \{1,\ldots,N\}$, with $m,N\in\mathbb{N}$ such that $m< N$. Selection procedure ...
7
votes
1answer
293 views

Raphael Douady's thesis: Applications du théorème des tores invariants

Raphael Douady's thesis, Applications du théorème des tores invariants, has been cited in numerous papers by many experts. According Wikipedia, he proves of the equivalence of KAM ...
5
votes
2answers
181 views

Probabilistic Interpretation of First Dirichlet Eigenvalue?

The first Dirichlet eigenvalue of a compact domain $\Omega\subset\mathbb{R}^n$ with smooth boundary is the smallest positive number for which there exists a non-trivial solution to $$ -\Delta\psi = ...
3
votes
1answer
285 views

A useful criterion in vector integration

I would like to know the proof of the following theorem: Consider two Banach spaces $X\hookrightarrow Y$ and $1<p,q\leq\infty$. Let $(f_n)_{n\geq 0}$ be a bounded sequence in $L^q(I,Y)$ and let ...
1
vote
0answers
160 views

Ideals with norm in arithmetic progression

Let K/Q be a number field extention. Is there an asymptotic formular for the numer of ideals $\sum\limits_{\substack{N(A)\leq x\\N(A)\equiv k(q)}}1$,where $(k,q)=1$ and $A$ runs over ideals in $O_K$. ...
5
votes
0answers
67 views

Short examples that are/are not quantum-ergodic

Are there any considerably short examples of manifolds that are/aren't quantum ergodic, or quantum unique ergodic? Note that a (compact) Riemannian manifold is said to be quantum ergodic if ...
1
vote
0answers
47 views

Can we make the weaker TPC tighter when we do the packing steiner trees?

The famous tree packing conjecture (TPC) posed by Gyarfas (see [1]) states: $\textbf{Conjecture 1}$. Any set of $n − 1$ trees $T_n, T_{n−1}, . . . , T_2$ such that $T_i$ has $i$ vertices pack into ...
5
votes
1answer
198 views

Can one prove that toric varieties are Cohen-Macaulay by finding a regular sequence?

It's well-known that if $P$ is a finitely generated saturated submonoid of $\mathbb{Z}^n$, then the monoid algebra $k[P]$ is Cohen-Macaulay (at the maximal ideal $m = (P-0)k[P]$). However, all proofs ...
2
votes
0answers
55 views

canonical bundle skew-symmetric determinantal varieties

By a skew-symmetric determinantal variety (over $\mathbb{C}$), I mean the projectivization of the set of skew-symmetric matrices of fixed size which rank is less than a given integer. More precisely, ...
1
vote
1answer
138 views

References about 3-manifolds

I am working on a subject of geometric group theory closely related to 3-manifolds, and in order to understand these links, I am seeking a good reference about 3-manifolds, as self-contained as ...
1
vote
1answer
236 views

Odd subgroup of $\mathrm{GL}(n,\mathbb{Z})$

The group $\mathrm{GL}(n,\mathbb{Z})$ acts on $(\mathbb{Z}/2\mathbb{Z})^n$ by right multiplication (the same kind of things can be done with left action). I denote by $H\subset ...
7
votes
1answer
187 views

worked out examples in borel-moore homology

I'm trying to learn about BM homology. I've found a few references and they are all quite abstract and high-powered. I am actually familiar with derived categories and sheaves so I don't mind thinking ...
10
votes
0answers
122 views

Maximality of linear orders in the Keisler order on theories

Recently Malliaris and Shelah (see their preprint http://math.uchicago.edu/~mem/Malliaris-Shelah-CST.pdf) have shown that theories with $SOP_2$ are maximal in the Keisler order. A preceding result of ...
6
votes
0answers
107 views

Zariski closure of orbits of real groups on complex flag manifolds

Let $G$ be a complex reductive algebraic group defined over $\mathbb R$, and $G_0$ its real points. Then the orbits of $G_0$ on $G/B$ need not be real algebraic subvarieties. Take $G=SL_2(\mathbb C)$, ...
5
votes
1answer
106 views

Attribution of an equivalence of the existence of omega-models of RCA0

There are many well-known equivalences in reverse mathematics between statements of the form "Every set is contained a countable coded $\omega$-model of $T$" and $S$, where $S, T$ are subsystems of ...
1
vote
0answers
153 views

$\mathfrak{q}$-ideal class bound

Let $K$ be a number field, $\mathcal{O}_K$ be its ring of integers. Let $\mathfrak{q}$ be a nonzero ideal in $\mathcal{O}_K$. The $\mathfrak{q}$-ideal class group consists of equivalence classes of ...
15
votes
5answers
2k views

Origin of exact sequences

I have seen exact sequences appearing a lot in algebraic texts with different purposes. But I've never seen names of the people associated with it. Also I don't understand what's so good about showing ...
5
votes
1answer
99 views

References to proofs of a theorem by Van Kampen-Flores

Theorem (Van Kampen-Flores 1930s) From any 7 points in four-dimensional space one can choose two disjoint triples such that the triangles with vertices at the triples intersect each other. This ...
1
vote
1answer
326 views

Study of convex polytopes via commutative algebra

Let $P \subset \mathbb{R}^d$ be any convex polytope with integral vertices, and let $M$ be the additive submonoid of $\mathbb{R}^{d+1}$ which is generated by $\{ (v,1) : v \in P \cap \mathbb{Z}^d \}$. ...
4
votes
1answer
106 views

Kolmogorov complexity of at least one string (from amongst those of a given length) is equal to its length

Is it true that for all strings of a given length at least one has its Kolmogorov complexity equal to its length ?(For any alphabet with more than 1 symbol) Is there a proof if the answer is in ...
1
vote
0answers
39 views

Reference Help: Matsuki duality Orbits

I'm studying the Matsuki duality of $G_0$-orbits and $K$-orbits over a flag manifold $G/P$ where $G$ is semisimple complex Lie group and $P$ is a parabolic subgroup. I would like to study some ...
1
vote
1answer
56 views

Strictly contracting elements in the center of a Levi subgroup

Let $G$ be a connected reductive group over a non archimedean local field $k$. Let $P \subset G$ be a parabolic subgroup with Levi decomposition $P=MN$, $Z_M \subset L$ be the center of $M$ and $S_M ...
0
votes
0answers
56 views

Sources in unimodular rows

I'm beginning to study more advanced material of module theory and I need to study more about unimodular rows. I would like a good introductory book or pdf speaking about unimodular rows with ...
8
votes
1answer
223 views

Explicit isomorphism for quaternion algebras over $\mathbb{Q}$?

It is known that the isomorphism class of a quaternion algebra $A=\binom{a,b}{K}$ over a number field $K$ is determined by the finite set of places $v$ of $K$ where $A\otimes_K K_v$ is a division ...
2
votes
1answer
151 views

Name and references for a “twisted” addition in a ring

This question may seem a little unmotivated, but it actually isn't something that just occurred to me out of nowhere. It stems from a discussion I had the other day with a friend and is directly ...
5
votes
2answers
171 views

Genus of Tutte-Coxeter Graph

What is the genus of the Tutte-Coxeter graph -- the incidence graph of the GQ of order 2? Seems like it should be well known, since nearly every other parameter for that graph is known, but I can ...
5
votes
1answer
178 views

Is there a holomorphic Morse-Bott lemma?

It asks for a generalization of the question in the post Normal form for a holomorphic Morse function Suppose $f$ is a holomorphic function on a complex manifold $M$ which has Bott type critical ...
7
votes
0answers
123 views

Phillips-Sarnak conjecture in higher dimension

The Phillips-Sarnak conjecture states that for a generic Fuchsian lattice the space of Maass cusp forms is finite-dimensional. Generic here means in particular non-uniform, non-arithmetic, no special ...
1
vote
0answers
151 views

An extrasensory perception strategy :-)

I asked this question at MSE some months ago but I received only partial answers, so I put it here. The following sounds nice for me and I spent a good time during the investigation. But I am a ...
2
votes
0answers
174 views

Looking for Soviet Math. Dokl [closed]

I'm a undergraduate student and I'm trying to study research level papers for the first time. I'm studying William Weiss's "Countably compact spaces and Martin's axiom" and he gives "Soviet Math. ...
11
votes
2answers
416 views

Postnikov's algebraic reconstruction of cohomology from homotopy invariants

In his short paper (1951) and longer monograph (1955), Postnikov introduced what I believe are now called Postnikov systems or towers. It is my understanding that Postnikov systems have since then ...
5
votes
2answers
278 views

Formal completion of the normal bundle

Let me for simplicity start with affine case. If $X=\operatorname{Spec}(A)$ is an affine variety $Z \subset X$ is a closed affine subvariety $Z=\operatorname{Spec}(A/I)$. What conditions are ...
0
votes
1answer
85 views

Characterizing Inf and Sup sets

Suppose $X$ is a set. Let $\Xi$ be the set of all pairs $(\mathcal A,\mathcal B)$ such that $$\mathcal A, \mathcal B \subseteq \mathcal P(X)$$ and for some partial order $\le$ on $X$, $\mathcal A$ is ...
7
votes
3answers
513 views

Consistency of Analysis (second order arithmetic)

Is there a proof of the consistency of Analysis (second order arithmetic), which is similar to Gentzen's proof of the consistency of arithmetic? Update: Which (different) methods can be used to ...
1
vote
0answers
71 views

unique types and decidability

Suppose $\mathcal{M}$ is an infinite structure which has the property that every type that is realised is realised uniquely. Also assume that every element of $\mathcal{M}$ is definable but there is ...
0
votes
0answers
92 views

A parabolic PDE with Lipschitz nonlinearity, how to obtain well-posedness?

Let $\Omega$ be a bounded smooth domain in $\mathbb{R}^n$ (or more generally a compact manifold). I'm interested in well-posedness (existence most importantly) of equations of the form $$u_t(t) - ...
3
votes
1answer
196 views

Colorful model theory

There are a number of concepts in model theory - often situated around Hrushovski's amalgamation method (see for instance http://math.univ-lyon1.fr/~wagner/nijmegen.pdf) - which are colorfully named: ...
3
votes
0answers
68 views

What do we know about the generalized eigenvalue problem involving a projector?

Consider a matrix $A\in\mathbb{R}^{n\times n}$ and a projector $P\in\mathbb{R}^{n\times n}$. Are there results regarding the generalized eigenpairs $(v,\lambda)$ of the generalized eigenproblem ...
4
votes
1answer
199 views

Perfect set property implies $\omega_1$ is a limit cardinal in $L$

Specker proved in 1957 that if in $V$ every set of real numbers has the perfect set property, than in $L$, $\omega_1^V$ is actually a limit cardinal. The original proof is in German, and I've been ...
0
votes
2answers
101 views

Poincaré bundle and Weil pairing for Abelian schemes

In which situations is there a Poincaré bundle for Abelian schemes? In [Mumford, Abelian varieties] only the case of Abelian varieties is treated. The same question for the Weil pairing ...
1
vote
0answers
21 views

Equivalence of Lp harmonic functions on the ball and a representation by harmonic homogeneous polynomials

In Harmonic function theory there is a theorem which say if $u$ is a harmonic function on $B\left(a,r\right)$, then there exist homogeneous harmonic polynomials $p_{m}$ in $\mathbb{R}^{n}$ such that ...
3
votes
1answer
296 views

Does there exist a function such that $\int_{\mathbb{R}_+^{\star} } t^nf(t)dt=0$? [closed]

Let $f\in C([a,b],\mathbb{R})$ such that $\displaystyle\int_{a}^{b} t^nf(t)dt=0$ for all integer n. We know that $f\equiv 0$. It's call Hausdorff theorem. This theorem is wrong on $\mathbb{R^+}$, a ...
4
votes
0answers
62 views

Reference for statement that almost every $n$-element partial order has trivial automorphism group

I'm looking for a reference for the statement that almost every partial order on $n$ elements has trivial automorphism group. I've been told that this is a folklore result. Does anyone know of a ...
7
votes
2answers
211 views

Cokernel of the stable J-homomorphism at odd primes

Where can one learn about odd-primary components of the cokernel of the stable J-homomorphism? According to wonderful Wikipedia article on Homotopy groups of spheres, the "hard" part of the stable ...
5
votes
0answers
57 views

K-Theory and completion [duplicate]

I vaguely remember the existence of a statement that relates the $K$-theory (in the sense of Quillen) of a noetherian local ring $A$ with maximal ideal $\mathfrak{m}$ with the $K$-theory of the ...
5
votes
0answers
64 views

Classifying two-faces of four-polytopes

Motivation: This question is related to my study of hyperbolic Coxeter polytopes. In general, if one put some restrictions on the type of their dihedral angles (say, all dihedral angles are equal to ...