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

learn more… | top users | synonyms

5
votes
1answer
216 views

Index of congruence modular subgroup of level (1,d)

Let $D = \text{diag}(1,d)\in M_{2}(\mathbb{Z})$ be a $2\times 2$ matrix, where $d$ is an odd integer. We define the subgroup $\Gamma_D\subset M_{4}(\mathbb{Z})$ as: $$\Gamma_D := \left\lbrace R\in ...
0
votes
0answers
46 views

What are the main open problems in the theory of quasigroups and loops?

What are the main open problems in the theory of quasigroups and loops? A short survey would be welcome. Thanks
6
votes
1answer
214 views

Group actions in a homotopy category

Let $M$ be a model category and $G$ a finite group, and equip the category $M^G$ of $G$-objects in $M$ with, say, a projective model structure. Then there is a canonical functor $$\mathrm{Ho}(M^G) ...
7
votes
1answer
175 views

Localizing 2-categories about a single morphism

This question is a straight-up reference request, but of course I will be grateful for an answer in the event that no references are readily available. Consider a strict $2$-category $\mathbf{C}$ and ...
4
votes
2answers
315 views

Finite groups factorized into two simple alternating groups

My research is somehow related to the following question : Describe and classify all finite groups $G$ such that $G=HK$ with $H \cap K=1$, where $H \cong A_m$ and $K \cong A_n$ for some integers $m, ...
2
votes
1answer
201 views

(Co)tangent complexes of quotient stacks

Let $X$ be an algebraic variety over a field $\mathbb{K}$ equipped with a right action of a smooth algebraic group $G$. One can form the quotient stack $[X/G]$. My question is probably quite ...
5
votes
1answer
383 views

A generalized Burnside's lemma

Let $G$ be a finite group acting on a set $X$, and let $S\subseteq G$ be a union of conjugacy classes. Then I believe I can prove: $$ \sum_{[x]\in X/G} \frac{|G_x \cap S|}{|G_x|} = \sum_{g\in S} ...
5
votes
0answers
180 views

Strong Markov property for Poisson point process

The question is thoroughly contained in the title. I just say that I would only like to find a reference for this question. I have searched in some books, to no avail. Here is what I mean exactly. ...
2
votes
0answers
74 views

What is the source of this simple lemma in harmonic analysis over compact groups?

I recently needed this simple fact of harmonic analysis: Let $G$ be a discrete abelian group and $X\subset G$ be a finite subset. Then for any $\epsilon>0$ the set $\Gamma_\epsilon=\{ ...
9
votes
5answers
969 views

Brief Introduction to Modular Forms

What are the best introductory texts on modular forms that are suited for a brief six week course intended for advanced undergraduates? The students will be quite sharp and as far as prerequisites go, ...
14
votes
1answer
356 views

Is there any publication of Bombieri about the standard conjectures on algebraic cycles?

In "Standard conjectures of algebraic cycles" Grothendieck says: "... These [Standard conjectures] are not really new, and they were worked out about three years ago independently by Bombieri and ...
1
vote
0answers
126 views

Axioms for a symmetric monoidal bicategory

I start reading the axioms for a symmetric monoidal bicategory. The axioms include so many diagrams to be satisfied. I am wondering if people really use these axioms directly to check a given data is ...
4
votes
1answer
124 views

CW complex with generalized cells

In the definition of CW complexes, all cells are homeomorphic to closed balls. I search for a generalized notion of CW complexes. In my application, the complexes are in fact finite. Is there a ...
4
votes
0answers
165 views

Which ring spectra have some kind of exponential map turning addition into multiplication?

This accepted answer to the question about $BU_\otimes$ made me recall that I want to read about this general phenomenon for a long time. What will follow is sort of vernacular but whether it can be ...
6
votes
1answer
145 views

Is the total space of a family of normal varieties a normal variety?

Let $f:X \rightarrow C$ be a flat morphism from a complex variety $X$ to a smooth curve $C$. If any fiber $X_{t}=f^{-1}(t)$ is a reduced normal projective variety, is the total space $X$ a normal ...
1
vote
0answers
68 views

Interesting fragments of first-order logic induced by sorting?

In first approximation, modal logic (I'm using the term loosely) can be understood as an interesting fragment of first-order logic (for simplicity I ignore e.g. how modal logic relates to ...
1
vote
0answers
208 views

Where can I find the article of A. Borel: “Values of zeta-functions at integers, cohomology and polylogarithms”? [closed]

Where on the internet can I find this article? I know that it is in this book: Current trends in mathematics and physics, Narosa, New Delhi, 1995.
0
votes
1answer
91 views

Non-convergence of ergodic measures with positive entropy

Let $T:X\to X$ be a continuous function on a compact metric space $X.$ Let $\mu$ be a $T$ invariant and ergodic probability measure on $X$ with strictly positive Sinai entropy $h_{\mu}(T).$ Let ...
1
vote
1answer
72 views

Example of non-convergence of iteration of measures

Let $T:X\to X$ be a continuous function on a compact metric space $X.$ Let $\mu$ be a $T$ invariant and ergodic probability measure on $X.$ Let $F:X\to X$ be a continuos transformation that commutes ...
-3
votes
1answer
329 views

Is SOC known to imply the Grand Riemann Hypothesis? [closed]

I'm currently working on a conditional proof of the Grand Riemann Hypothesis, which is based on the assumption that every field automorphism of $\mathbb{C}$ that commutes with an element of the ...
2
votes
0answers
86 views

Chern-Weil theory for degenerated metric

If $\omega$ is a Kähler metric on a compact complex manifold $X$, the standard Chern-Weil theory says that the Chern classes $c_{i}(M)$ can be represented by forms involving the curvature of ...
0
votes
1answer
101 views

Name search for special Linear Integer Programm

I am looking for a name for the following question in literature! (and if you know it, then it would be great) I couldn't find it and due to wide audience here, presumably you know more. Thank you ...
0
votes
1answer
184 views

Is there is a known relation or expression containing the algebraic rank $r$?

Let $$L(C,s)=\sum_{n=1}^\infty \frac{a_n}{n^s}$$ be the Dirichlet series of the Hasse--Weil L-function of an elliptic curve $C$ over $ℚ$. The modularity theorem implies that $L(C,s)$ is the ...
0
votes
0answers
16 views

C-Periodic boundary conditions

I'm working with linear chain of strongly correlated electrons. These types of models have problems due to finite size effects, this leads one to consider C-Periodic boundary conditions as an attempt ...
6
votes
2answers
225 views

Conjectured congruence for the Apery numbers

Numerical evidence for the first hundred Apery numbers $$A_n=\sum\limits_{k=0}^n\binom{n}{k}^2\binom{n+k}{k}^2$$ suggests the following congruence relation $$A_n\equiv 0\; (\mathrm{mod}\; ...
1
vote
1answer
168 views

Countable residually finite abelian groups

Is there a countable abelian group for which its subgroups are exactly all of the countable "reduced" abelian groups? (Reduced means that its divisible subgroup is zero) Is the following group a ...
2
votes
0answers
70 views

relative cohomology $H(X,D)$ of a pair in Weil cohomology theory

In algebraic topology, one defines relative cohomology groups $H(X,A)$ of a pair of spaces $A\subset X$. Is there an analogue in algebraic geometry of cohomology of a pair of schemes? For example, ...
2
votes
0answers
49 views

Generalized separating systems

We call a set system $\mathcal{A}$ of subsets of the $n$ element universe $U$ a separating system if for any pair of elements $x,y \in U$ there is at least one set $A \in \mathcal{A}$ such that either ...
1
vote
0answers
125 views

What is a morphism of $B_\infty$ algebra

Let $k$ be a commutative ring and $C$ a $ \mathbb{Z}$ graded $k$ module. A $B_\infty$ structure on $C$ is the datum of a differential and a multiplication on $ BC:= \bigoplus^\infty_{i =0} ...
7
votes
2answers
126 views

Bounds on chromatic number of $k$-planar graphs

A $1$-planar graph can be drawn in the plane so that each arc is crossed at most once by another arc. A $k$-planar graph can be drawn so that each arc is crossed at most $k$ times. Planar graphs are ...
0
votes
0answers
89 views

topological space of Wang Tile

When trying to reprove a theorem in Wang tile: An established proof in Wang Tile which I doubt , a few notions are provided which I would like to seek for more information: For a given set of blocks ...
2
votes
1answer
84 views

dimensions of strata of Pfaffian varieties

Let $V$ a complex vector space of dimension $2n$. Let us consider $W=\wedge^2V$ and the Pfaffian variety $Pf\subset \mathbb{P}W$ that parametrize degenerate skew-symmetric matrices. $Pf$ is naturally ...
0
votes
0answers
66 views

Ring structure for $K^{-1}$?

My questions are whether there exists a product structure for $K^{-1}(X)$? Here $K^{-1}$ is the odd topological $K$-group, and $X$ is a compact space (or a manifold), say. If such a ring structure ...
2
votes
0answers
32 views

Where to read about this kind of “measure of irredundancy” of a set from a family of sets?

Studying a very practical problem from psychometrics, I encountered the following construction. Let $(X,\mu)$ be a measure space; if preferred, you can presume $\mu$ is a probability measure. In any ...
3
votes
3answers
171 views

Time-inhomogeneous Markov Chains

I'm trying to find out what is known about time-inhomogeneous ergodic Markov Chains where the transition matrix can vary over time. All textbooks and lecture notes I could find initially introduce ...
3
votes
3answers
730 views

An established proof in Wang Tile which I doubt

When I was reading the paper: Wang, Hao. "Notes on a class of tiling problems." Fundamenta Mathematicae 82.4 (1975): 295-305. from http://matwbn.icm.edu.pl/ksiazki/fm/fm82/fm82119.pdf I could not ...
1
vote
1answer
197 views

Inducing a Monoidal Structure using an Equivalence of Categories [closed]

Given an equivalence of categories $C \equiv D$, such that $C$ has a monoidal structure, is it clear that we can use the equivalence to induce a monoidal structure on $D$. Is there a standard ...
2
votes
1answer
266 views

Is there an english translation of Delignes “La conjecture de Weil pour les surfaces K3.”?

The title is pretty self explanatory: I'm looking for an english translation of Delignes inventiones paper "La conjecture de Weil pour les surfaces K3." Anyone know if such a thing exists? Thanks!
0
votes
1answer
169 views

A very natural question in weak* topology [closed]

Can you provide me a counter example for this. Suppose that I have a sequence of probability measures $(\mu_{r,t})_{r,t>0}$ on a compact space metric $X.$ Suppose additionally that: there exists ...
8
votes
4answers
390 views

Action of a Lie group with finitely many orbits

EDIT: Let a real Lie group $G$ act on a smooth manifold $M$ with finitely many orbits such that each orbit is locally closed ($M$, but not $G$, may be assumed to be compact in my case). Let ...
7
votes
1answer
272 views

What is the total polarization of the determinant?

Let $A\in\mathfrak{gl}(\mathbb{R},n)$ be an endomorphism, and think up to conformal factors (in particular, $\Lambda^n\mathbb{R}^n$ will be the same as $\mathbb{R}$). By the total polarization ...
8
votes
1answer
220 views

Shriek push-forward for parameterized spectra

In May and Sigurdsson's Parameterized Homotopy Theory, Proposition 2.2.11, four isomorphisms of functors are given. For a pullback square of base spaces $C=holim(A\overset{f}\to B\overset{j}\leftarrow ...
4
votes
1answer
189 views

Recommended textbooks for Hamiltonian group actions?

I am doing a project on Hamiltonian group actions on symplectic manifolds, and my supervisor was able to list several good books on Riemannian geometry to start me off, but he didn't know of any ...
2
votes
2answers
96 views

formula for repeated finite differences

I am looking for a proof of a well-known fact, whose proof must be very easy, though I've been struggling to find it. Let $\Delta$ be the map from real-valued functions of a real variable, given by ...
1
vote
1answer
126 views

Link between integral points on varieties and solutions to Diophantine equations

Let $k$ be a number field, $S$ a finite set of places of $k$ including the infinite ones and $F(X_1,\dots,X_n)$ a polynomial in $k[X_1,\dots,X_n]$. I am looking for notes, books or surveys detailing ...
9
votes
3answers
252 views

Dimensions of self-affine sets

Let $A$ be a $2\times 2$ matrix which we assume to be contracting, i.e., the exists $\alpha\in(0,1)$ such that $$ \|A {\mathbf x}\|_2\le \alpha\|{\mathbf x}\|_2,\quad \forall {\mathbf x}\in\mathbb ...
7
votes
1answer
346 views

Demuth's theorem in set theory

I am quite sure the following fact must have been known for set theorists, though I could not find it anywhere. If $r$ is random over $L$ and $x\in L[r]\setminus L$, then there must be some real ...
0
votes
0answers
29 views

Approximation with Predefined Topology of Niveau Sets

Problem given are a finite, connected, undirected and, cycle-free graph (i.e. a "tree") $T(V,E)$, of which one of the vertices (w.l.o.g. $v_0$) is defined to be the root. a planar imbedding ...
11
votes
3answers
1k views

Source of quotation about the waste-baskets of physicists

In an article I'm writing I want to quote (with attribution) the original version of an aphorism that says that one can often find mathematical gold in the waste-baskets of physicists. Would someone ...
9
votes
0answers
278 views

Short proof of $\frak p=t$

It is known for a while now that $\frak p=t$, as a result of Malliaris-Shelah. The original paper draws from model theoretic methods. I've heard rumors that there was a proof which was purely set ...