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

**5**

votes

**1**answer

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

**0**answers

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

**1**answer

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

**1**answer

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

**2**answers

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

**1**answer

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

**1**answer

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

**0**answers

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

**0**answers

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

**5**answers

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

**1**answer

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

**0**answers

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

**1**answer

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**1**answer

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

**1**answer

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

**1**answer

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

**0**answers

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

**1**answer

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

**1**answer

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

**0**answers

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

**2**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**0**answers

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

**2**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**3**answers

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

**3**answers

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

**1**answer

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

**1**answer

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

**1**answer

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

**4**answers

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

**1**answer

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

**1**answer

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

**1**answer

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

**2**answers

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

**1**answer

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

**3**answers

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

**1**answer

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

**0**answers

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

**3**answers

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

**0**answers

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 ...