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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Abelian subvarieties of abelian varieties --- reference request

This question may be too naive, in which case I apologise in advance. Anyway, it is a well-known fact (see e.g. Milne's notes) that any abelian variety A has only finitely many direct factors up to ...
user avatar
6 votes
3 answers
554 views

profinite spaces coming from profinite groups

This is probably well-known: Does every nonempty profinite space occur as the underlying space of a profinite group? If not, which conditions have to be imposed? - Is every profinite group ...
Martin Brandenburg's user avatar
6 votes
1 answer
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Topological entropy of semi-conjugated dynamical systems

Let $(X,T)$ and $(Y,G)$ be topological dynamical systems. If $(Y,G)$ is a factor of $(X,T)$ it is well known and easy to proof that $h(G)\le h(T)$ , where $h$ denotes the topological entropy. If the ...
Jörg Neunhäuserer's user avatar
6 votes
1 answer
207 views

Classification of algebraic groups of the types $^1\! A_{n-1}$ and $^2\! A_{n-1}$

This seemingly elementary question was asked in Mathematics StackExchange.com: https://math.stackexchange.com/q/4779592/37763. It got upvotes, but no answers or comments, and so I ask it here. Let $G$ ...
Mikhail Borovoi's user avatar
6 votes
1 answer
318 views

Does $\overline{\mathbb{C}P^2 \setminus B^4}$ embed (smoothly/topologically) in $\mathbb R^5$?

Question: Does $\overline{\mathbb{CP}^2 \setminus B^4}$ (that is the closure of complex projective plane minus a 4-ball) embed (smoothly/topologically/piecewise linearly) in $\mathbb R^5$? Background: ...
Martin Tancer's user avatar
6 votes
1 answer
478 views

A numerical matrix of power sum polynomials

Let $p_i=x_1^i+x_2^i+\cdots+x_m^i=\sum_{k=1}^mx_k^i$ be the power sum polynomials. Then, the determinant of the $m\times m$ Hankel matrix $M_m=(p_{i+j-2})$, for $1\leq i,j\leq m$, has a neat ...
T. Amdeberhan's user avatar
6 votes
1 answer
257 views

A Sauer-Shelah-like lermma for prefix tree

I proved a variant of the Sauer-Shelah lemma and I was wondering if something like that is already known. Let $S \subseteq \{0,1\}^n $. We say that a set of coordinates $K \subseteq [n]$ is shattered ...
Or Meir's user avatar
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428 views

Where can I find a definition of $\underline{H}^p(X, \mathscr{F})$?

Let $X$ be a topological space and $\mathscr{F}$ a sheaf on $X$. In the paper Tropical cycle classes for non-archimedean spaces and weight decomposition of de Rham cohomology sheaves by Yifeng Liu, ...
Jakob Werner's user avatar
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1 answer
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Are infinitary monads monadic?

As discussed here, Are monads monadic?, in "On the monadicity of finitary monads" by Steve Lack, the following is shown, the forgetful functor from $Mnd_f(C) \rightarrow Endo_f(C)$ is ...
Ilk's user avatar
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Norm of contragredient of unitary representations of compact quantum groups

Maybe the answer to the following question is known but I am unable to find it in the literature. Anyway, let me begin my question by fixing some notations and terms. Let $G = (A, \Delta)$ be a ...
Hua Wang's user avatar
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1 answer
596 views

The history and original paper of the Rosser–Iwaniec sieve

I'm trying to find Rosser's original paper where he introduces his eponymous sieve. I've already found https://arxiv.org/pdf/math/0505521 (where the reference isn't given, but where it is indicated ...
Cloudscape's user avatar
6 votes
1 answer
175 views

Tensor representations of the quantum algebra $U_q(\mathfrak{sl}(2))$ at the roots of unity

I'm trying to understand how the representation theory of $U_q(\mathfrak{sl}(2))$ works and I had a look to some books and lecture notes available on the internet. The case of $q^m\neq1$ is discussed ...
pomello gaudente's user avatar
6 votes
1 answer
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Bounding size of partial difference sets given size of partial sumsets

In this paper by Katz and Tao, the following bounds were established. Let $A,B$ be finite subsets of an abelian group, with $|A|,|B|\le N$. We fix some $G \subset A\times B$. We define $C = \{a+b:(a,b)...
Zach Hunter's user avatar
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Rickard's strengthening of Broué's abelian defect group conjecture and the lifting of some equivalences up to splendid derived equivalences

Let $G$ be a finite group. Let $p$ be a prime dividing $|G|$. Let $K:=\overline{\mathbb{F}_p}$. Let $b$ be a $p$-block of $G$ with abelian defect group $D$. Let $H:=N_G(D)$. Let $c$ be the Brauer ...
Bernhard Boehmler's user avatar
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1 answer
564 views

Does the purported proof of Rota's conjecture provide an algorithm for calculating the forbidden minors of matroids over arbitrary finite fields?

About six years ago there was a proof announced and later outlined in a notice from AMS. However right now I can only seem to find forbidden minor characterizations for matroids linearly ...
Ethan Splaver's user avatar
6 votes
1 answer
244 views

A unique equilibrium state which does not have Gibbs property

Let $T:\Sigma \rightarrow \Sigma$ be a topologically mixing subshift of finite type and let $f:\Sigma \rightarrow \mathbb{R}$ be a continuous functions over $(T, \Sigma)$. Assume that there is a ...
Adam's user avatar
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6 votes
1 answer
490 views

Mori's cone theorem

I need the proof (reference) of Mori’s theorem about this implication : Let $X$ be a projective complex manifold. If $X$ contains no rational curves, then $K_K$ is nef.
Kamel's user avatar
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1 answer
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What is known about the functional square root of the Riemann zeta function?

Let us consider the Riemann zeta function $\zeta(s)$, where $s$ can take on values on the domain $\mathbb{R}_{>1}$: $$\zeta(s) := \sum_{n=1}^{\infty} \frac{1}{n^{s}} .$$ I wonder what is known ...
Max Muller's user avatar
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6 votes
2 answers
232 views

Fibre preserving maps of Borel constructions

Let $G$ be a discrete group with universal principal bundle $EG\to BG$, and let $X$ and $Y$ be left $G$-spaces. An equivariant map $\overline{f}:X\to Y$ induces a fibre-preserving map $f:EG\times_G X\...
Mark Grant's user avatar
6 votes
1 answer
238 views

Arens regularity of Banach algebras

I was trying to learn the concept of Arens regularity of Banach algebras from T.W Palmers book -"Banach algebras and the general theory of $*$-algebras". There he have discussed the Arens regularity ...
NewB's user avatar
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3 answers
599 views

Electromagnetism as a $U(1)$-gauge theory

I would like to learn gauge theory, starting from the simplest case. I have heard that I should start with electromagnetism, which is just the $U(1)$-gauge theory. All the references I know are ...
Student's user avatar
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6 votes
1 answer
241 views

Concrete example to illustrate the theory about blocks of groups with cyclic defect groups

I'd like to to have a concrete example to illustrate the theory about blocks of groups with cyclic defect groups. Thus, I am looking for a finite group $G$ and a prime $p$ dividing $|G|$ satisfying ...
Bernhard Boehmler's user avatar
6 votes
2 answers
270 views

RSK and crystal operators

Is there a good reference on how RSK (and the 3 other variants) interact with crystal operators on the semi-standard tableaux $(P,Q)$ in the image? That is, we have biwords, $W$ which are in ...
Per Alexandersson's user avatar
6 votes
1 answer
330 views

Can the number of solutions to a system of PDEs be bounded using the characteristic variety?

I've recently come across a system of PDEs which I'd like to understand better. The particular system I'm interested in locally solves for a 2-dimensional Riemannian metric as the Hessian of a ...
Gabe K's user avatar
  • 5,364
6 votes
2 answers
1k views

Functorial cones

This is probably more a reference request than a real question. I was studying dg-categories in order to understand how one can derive a functorial cone construction when a triangulated category (...
Federico Barbacovi's user avatar
6 votes
1 answer
630 views

Is there an English translation of Laumon's proof of geometric Langlands for $\mathbb{G}_m$?

I'd like a detailed proof in English of Laumon's proof that the two Fourier-Mukai transforms taking the derived category of quasicoherent sheaves on $\mathbb{G}_m$-local systems of a curve $X$ to the ...
Exit path's user avatar
  • 2,969
6 votes
1 answer
204 views

Is the projection onto the regular image an epimorphism?

Let $f:X\to Y$ be a morphism in a category $\mathcal{C}$. Let $m:I\hookrightarrow Y$ be the regular image of $f$. This means that $f$ can be written as $f=m\circ e$, with $m$ regular mono (i.e. being ...
geodude's user avatar
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6 votes
1 answer
268 views

Schutzenberger's evacuation and $\mu$-coefficient of Kazhdan–Lusztig polynomials

$\def\SYT{\mathrm{SYT}}\def\RSK{\mathrm{RSK}}\DeclareMathOperator\evac{evac}$Let $\mathfrak{S}_n$ be the symmetric group, $\SYT_n$ be the set of standard young tableaux of size $n$. For $u\in \...
Sylvester W. Zhang's user avatar
6 votes
1 answer
241 views

Nash embedding for complete manifold

I, ask my question as a comment in this post. Without answer I post a more detailed version. I am looking for a reference about $C^\infty$ Nash isometric embedding for non compact manifold. My ...
Paul's user avatar
  • 914
6 votes
1 answer
576 views

The Gauss Circle Problem asymptotic in dimension

The circle problem in $k$ dimensions: "For $n>0$, how many points $z\in \ \mathbb{Z}^k$ have $\|z\|^2\leq n$?" For large $n$, the answer is $\approx n^{k/2}\cdot \operatorname{Vol}(B^k(0,1))+\...
Christian Chapman's user avatar
6 votes
1 answer
295 views

Citations graphs: what is known?

There has been much research related to web graphs and social graphs. They can be thought of as a kind of random graphs, but the point is that they are different from the well-known Erdős–Rényi model. ...
Alexander Chervov's user avatar
6 votes
2 answers
588 views

Interpolation space between $L^1\cap L^2$ and $L^1$

In the paper of Bourgain, the way equation (3.78) is deduced from (3.69) and (3.76) seems via the following interpolation result. Let $(X,\mu)$ and $(Y,\nu)$ be two measure spaces and let $T$ be a ...
shrinklemma's user avatar
6 votes
1 answer
348 views

Homotopy cosheaf?

Let $C$ be a site, $\mathbf{S}$ some ($\infty$-? homotopy?) category of spaces. Question. What do you call a (covariant!) functor $F:C\to \mathbf{S}$ enjoying the following property: for every ...
Piotr Achinger's user avatar
6 votes
2 answers
573 views

Online Interactive mathematics games for mathematicians or mathematicians-to-be!

I am aware that this is not a research level mathematics question. Also, it would not have a single answer (if any) and yet, I hoping that it will be considered as a community wiki question worthy of ...
6 votes
2 answers
627 views

Wiener Measure measure on functions?

I know that the Wiener measure for the Brownian motion $\{B_t\}_{t\ge 0}$ on the probability space $(\Omega, \mathscr{F},P)$ can be defined as $\mu=P\circ B^{-1}$ acting on the sigma-algebra generated ...
Quantum spaghettification's user avatar
6 votes
1 answer
825 views

Rice's theorem in type theory

From the formula $$\forall f\colon A\to A\,\exists x\colon A\,(f(x)=x)$$ we can get the scheme $$\forall x\colon A\,(\phi(x)\vee\neg\phi(x))\Rightarrow\forall x\colon A\,\phi(x)\vee\forall x\colon A\,\...
George Cherevichenko's user avatar
6 votes
1 answer
479 views

Fourth cohomology of the modular group

Is $H^4(PSL(2,\mathbb{Z}),\mathbb{Z})$ known? I ask this in response to the recent calculation of the same cohomology group for $\mathrm{Co}_0$ and $\mathrm{Co}_1$.
David Roberts's user avatar
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6 votes
1 answer
965 views

What did Zermelo say he was hoping for on the consistency of set theory?

Question. What precise things are known about what Zermelo is hinting at in the below citation? What are scholarly references on Zermelo's own attempts at proving consistency of his axioms? What did ...
Peter Heinig's user avatar
  • 6,001
6 votes
1 answer
677 views

Thick subcategories

I hope this question is not too trivial for mathoverfolw. Let $R$ be a commutative ring (with $0\neq 1$) and $D_{Perf}(R)$ the triangulated category of perfect complexes. Let $C$ be a thick ...
M.O.'s user avatar
  • 125
6 votes
1 answer
357 views

Evolving curves by Alexander Polden

I am writing a piece on curve shortening flow and lots of my sources have referenced Alexander Polden's honours thesis 'Evolving Curves' from the Australian National University. I have tried to find ...
jl2's user avatar
  • 235
6 votes
1 answer
251 views

Every PD group is $\pi_1$ of an aspherical manifold

It is conjectured that for a discrete, finitely presented group $G$ such that $BG$ satisfies Poincaré duality, there actually exists a closed manifold $M$ which is homotopy equivalent to $BG$. This ...
Jens Reinhold's user avatar
6 votes
1 answer
881 views

Total space of canonical bundle as resolution of singularity

We know for $Y=\mathbb{P}^n$, the total space of the canonical sheaf $Tot(\omega_Y)$ is the resolution of $\mathbb{C}^{n+1}/\mathbb{Z}_{n+1}$ where the generator acts as scalar matrix of multiplying a ...
Xuqiang QIN's user avatar
6 votes
2 answers
820 views

A dynamical system defined by the Riemann zeta function

Let $\zeta$ be the classical Riemann zeta function. We define a differential equation on $\mathbb{R}^{2} \setminus \{1\}$ by $\dot Z= \zeta(Z)$. From a foliation point of view this vector ...
Ali Taghavi's user avatar
6 votes
1 answer
295 views

Reference request to proof that H$^2(\Gamma, \mathbb{Q}/\mathbb{Z}) = 0$

Does anyone maybe have a reference to the proof of the following result by Tate? Let $\Gamma$ be the absolute Galois group of the rationals. Then the second cohomology group (for trivial $\Gamma$-...
JH_94's user avatar
  • 63
6 votes
1 answer
364 views

Embedding a cancellative monoid into another in such a way that a prescribed element becomes left-invertible

Let $\mathbb A = (A, +_A)$ be a cancellative, but possibly non-commutative, monoid with identity $0$, and fix an element $x \in A$. Does there always exist a cancellative monoid $\mathbb B = (B, +)$ ...
Salvo Tringali's user avatar
6 votes
1 answer
268 views

Is there a canonical split signature metric on $\mathbb{P}^n\times\mathbb{P}^{n\,\ast}$?

Let $$ M:=\{(P,\pi)\mid P\not\in\pi\}\subset\mathbb{P}^n\times\mathbb{P}^{n\,\ast} $$ be the open and dense (and as such $2n$-dimensional) subset of non-incident point-hyperplane pairs. If $P=\mathbb{...
Giovanni Moreno's user avatar
6 votes
1 answer
249 views

Fundamental class in $KO[1/2]$

Let $M^m$ be an oriented Riemannian manifold. The signature operator associates to $M$ a class $\Delta_M\in KO_m(M)[1/2]$. I have two questions about this class $\Delta_M$: Rationally, $\Delta_M$ is ...
user81127's user avatar
6 votes
1 answer
1k views

Derivatives of theta functions at zero

Let $L$ be a line bundle over complex elliptic curve, $\deg L = k>0$. Theta functions $$ \theta_s(z;\tau)_k=\sum_{r\in \mathbb{Z}} e^{\pi i [(\frac{s}{k} + r)^2 k \tau + 2kz(\frac{s}{k}+r)]}, \...
Sasha Pavlov's user avatar
  • 1,535
6 votes
1 answer
192 views

Radon transform between affine grassmannians

Let $\overline{GR}(n,k)$ be the manifold of all affine k-dimensional subspaces in $R^n$, and let $R:C^{\infty}_c(\overline{GR}(n,k))\to C^{\infty}_c(\overline{GR}(n,l))$, $0\le k<l\le n-1$, be the ...
Dmitry Ryabogin's user avatar
6 votes
1 answer
1k views

Kullback Leibler "variance": does that divergence have a name?

If you consider two probability distributions $p$ and $q$, one way to measure the distance between the two is the Kullback-Leibler divergence: $$KL(p,q)=\int p \log (p/q) = E_p(\log p/q)$$ and this ...
Guillaume Dehaene's user avatar

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