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

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2
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0answers
78 views

Reference for Arakelov's theorem: $K^2_f=0$ iff $f$ is locally trivial

Let $f:X\longrightarrow B$ be a family of curves, with $f$ relatively minimal, over a fixed curve $B$ ($B$ is projective, irreducible and smooth). The fibration $f$ is said locally trivial if all ...
2
votes
2answers
103 views

boundary homomorphism in the homotopy exact seqeunce of principal $SO(9)$ bundle over $S^8$

Consider principal $SO(9)$ bundles over $S^8$.They are in 1-1 correspondence with $$[S^8,BSO(9)]\cong \pi_7(SO(9))\cong \mathbb{Z}$$ Now pick up one such bundle $\xi$,we have the long exact sequence ...
5
votes
1answer
87 views

Symmetry type of non-cohomological automorphic forms

By Katz-Sarnak philosophy a family of $L$-functions would have a symmetry type which would reflect the statistics of $L$-functions, such as low lying zeros and moments. Shin-Templier's paper on ...
0
votes
0answers
65 views

When an integral with respect to a Poisson point process is finite?

Let $N(ds,dv)$ be a Poisson measure on $\mathbb{R} _+ \times \mathbb{R} _+$ with intensity $dsdv$. Let $N = \sum\limits \delta_{(s_i,v_i)}$. Assume that $N$ is compatible with a filtration $\{ ...
2
votes
1answer
198 views

What happens to the cohomology ring after a “flip-flop”?

I've been trying to understand what happens to the cohomology ring (say with coefficients in $\mathbb{R}$) of a smooth complex projective manifold after blowing up along a smooth complex submanifold. ...
8
votes
3answers
197 views

How do small central extensions drop the dimension of a faithful representation?

Apologies in advance that this is a very soft question. I might be talking complete nonsense. But I hope I am talking about something that has even been studied... I am interested in the phenomenon ...
8
votes
2answers
233 views

Implicit Function Theorem on Singular Varieties

Let $X$ and $Y$ be two complex reduced affine algebraic or analytic varieties, possibly singular. Take a regular proper function $$f\colon X \to Y $$ and assume that it is bijective at the level of ...
5
votes
1answer
136 views

Analytic perturbation of eigenfunctions

Consider a domain $\Omega_0 \subset \mathbb{R}^n$, and deformations of $\Omega_0$, called $\Omega_t$, obtained by a one-to-one mapping $x \mapsto x + t\varphi (x)$, where $\varphi$ is smooth. It is ...
7
votes
1answer
206 views

A proper smooth surface is projective

My question is a reference request for the following fact: if $k$ is a field and $X$ a proper smooth surface over $k$, then $X \rightarrow \mathrm{Spec}\, k$ is projective. Where is this well-known ...
7
votes
2answers
479 views

Most dense subset of numbers that avoids arbitrarily long arithmetic progressions

The famous Green-Tao theorem says that there exist arbitrarily long sequences of primes in arithmetic progression. I am wondering: How dense can a subset $S \subset \mathbb{N}$ be and still avoid ...
1
vote
0answers
38 views

How often can a single length occur as a boundary distance?

Given a bounded domain $\Omega\subset\mathbb R^n$ ($n\geq2$), how often can a single real number $r>0$ appear as a distance of two points on $\partial\Omega$? We can make any assumptions about the ...
3
votes
0answers
116 views

Prime zeta zeros - reference

Is there an online repository for zeros of the prime zeta function? I looked at the Yahoo group Prime numbers and primality testing listed on the MathWorld notebook for the prime zeta function, but ...
1
vote
0answers
78 views

Best constant for Maier's theorem?

Maier proved that, for fixed $\lambda>1,$ $$ \limsup_{x\to\infty}\frac{\pi(x+\log^\lambda x)-\pi(x)}{\log^{\lambda-1}x}>1 $$ and in particular $$ \limsup_{x\to\infty}\frac{\pi(x+\log^\lambda ...
5
votes
1answer
352 views

Structure of the automorphism group of a Riemann surface

I was wondering if anything is known about the possible structure of $\mathrm{Aut}(S)$ for a Riemann surface $S$. More precisely, are there known obstructions for a finite group $G$ to be such an ...
1
vote
1answer
135 views

Some general properties of arithmetic groups of simplest type

I'm working in the area of arithmetic Kleinian groups (as discrete groups of motions of hyperbolic 3-space). For the more general case of hyperbolic $n$-space, there is a particular class of ...
4
votes
1answer
298 views

Boardman-Vogt tensor product

Let $\mathbf{sSet}$ be the model category of simplicial sets and $\mathbf{Op}$ the model category of symmetric operads. Equipped with Boardman-Vogt tensor product $ \otimes_{BV}$, the category ...
0
votes
0answers
93 views

The fundamental group of the complement of codimension 2 submanifold

Suppose that $M^n$, $V^{n+2}$ are connected, compact smooth manifolds. Let $f\colon M^n\to V^{n+2}$ is a smooth embedding. Let $K_f$ be the kernel of the inclusion induced homomorphism ...
0
votes
0answers
103 views

Construction of Penrose Tiling (P3) from Wieringa Roof [closed]

I am trying to find sources detailing the construction of the Wieringa* Roof with the purpose of projecting the roof onto the plane and generating a Penrose Tiling (P3). The method can be seen in ...
5
votes
1answer
150 views

Did Lucas discover Lucas circles?

MathWord's article on Lucas circles traces the name to a little-known 1973 publication. These interesting circles have found their way into several 21st century publications, including the online ...
2
votes
0answers
121 views

How to write BRST-BV for dg-Lie?

The usual BRST-BV implements a Lie algebra and its module in terms of ghosts, etc. Where is there written a corresponding formula incorporating the differential of a dg Lie algebra and module?
2
votes
1answer
101 views

Compact radial Sobolev embedding $H^1_{rad}\hookrightarrow L^p$

I want to show: Let $N\geq 2$ and $2< q <2^\ast$. Then the embedding \begin{align} H^1_{\text{rad}}(\mathbb{R}^N)\hookrightarrow L^q(\mathbb{R}^N) \end{align} is compact. I was able to show ...
2
votes
1answer
77 views

Stirling numbers of the second kind with maximum part size

The stirling number of the second kind $S(n,k)$ counts the number of partitions of the set $[n]$ into $k$ non-empty parts. I found a definition for the numbers called the $r$-associated stirling ...
1
vote
0answers
121 views

Kwantitatieve Methoden [closed]

I'm looking for one article (Eilers P. H. C., 1987, Asymmetric least squares: New faces of a scatterplot. Kwantitatieve methoden 8, 45-64) and since I was not able to find it for some time, I'm asking ...
5
votes
1answer
330 views

Alternate proof of Morley's theorem?

I'm trying to understand the result given in the first box at slide 45 of this talk. Specifically: 1) What is the source cited? I have not been able to find any article by Keisler, Chudnovsky and/or ...
4
votes
0answers
90 views

Improvements of the Reidemeister-Schreier index formula for particular classes of groups

I have a couple of questions regarding possible improvements of the Reidemeister-Schreier index formula: let $G$ be a $d$-generated group and let $H$ be a subgroup of $G$, then $$d(H) \le (d-1) ...
5
votes
2answers
196 views

Primitive Recursive Arithmetic via Universal Algebra

From the wikipedia article on Primitive Recursive Arithmetic (see http://en.wikipedia.org/wiki/Primitive_recursive_arithmetic): "Primitive recursive arithmetic, or PRA, is a quantifier-free ...
5
votes
3answers
416 views

Survey of Engineering Problems for Mathematicians [closed]

I am looking for survey-books on open math (esp. probability) problems from engineering fields but phrased in mathematical language. There are hundreds of specialized math-engineering books out ...
1
vote
0answers
43 views

Fractional Poincare inequality on closed manifold

Let $u \in H^{\frac 12}(M)$ on a compact closed Riemannian manifold. Can someone refer me to a source where the inequality $$\lVert u - \bar u \rVert_{L^{2^*}} \leq C|u|_{H^{\frac 12}}$$ is proved, or ...
4
votes
1answer
178 views

Explicit bounds for transfer results in algebraic geometry

Assume you have an ideal $I\subseteq\mathbb{Z}[X_1,\ldots,X_n]$ of the polynomial ring in $n$ variables over the integers. For any field $\Bbbk$, I can consider the ideal ...
2
votes
0answers
92 views

Examples of Geometric Constructions in Higher Dimensions

The classical problem of geometric construction seems to be restricted to planar Euclidean Geometry with straight edge and compass as the only admissible "construction-tools". I would like to ...
0
votes
1answer
119 views

Hodge structure of relative cohomology groups

I need a hint or a good reference for definition of mixed Hodge structure on the relative cohomology groups ($\mathrm{H}^*(X,Y)$, $Y\subset X$ a closed subvariety of a comolex quasiprojective variety ...
0
votes
0answers
17 views

On a tower of strongly normal extensions

Where I could see the following statement? Let $K\subset L\subset M$ be a tower of the strongly normal extensions of differential fields. If $M$ is weakly normal over $K$, then $M$ is strongly ...
3
votes
1answer
200 views

Was $\Sigma x$ used as quantifier?

Kurt Gödel in 1931 used $x\Pi a$ where we in contemporary notation would use $(\forall x) A$ or $(x)A$, and $Ex a$ where we would use $(\exists x) A$. I believe that I remember that $\Sigma xA$ has ...
1
vote
0answers
55 views

Uniqueness of analytic center manifold

In a book, i have read a remark which says that the center manifold of an equilibrium point of a differential equation is not unique in general but is unique in the class of analytic manifold. The ...
0
votes
0answers
78 views

Summing a function at integer points

For a real function $f$ defined on the reals, and real $y$, define the 2-way infinite sum $$ F_f(y) = \sum_{i\in\mathbb Z} f(y+i). $$ If $F_f(y)$ is defined for all $y$, it is periodic of period 1. ...
0
votes
0answers
39 views

Interpolation of Banach spaces: theta = 0, 1

Let $A_1 \subset A_0$ be Banach spaces with continuous embedding. Is $(A_0, A_1)_{i, \infty} = A_i$ for $i =0, 1$, with equivalent norms? Here, $(\cdot, \cdot)_{\theta,p}$ denotes the $K$-method of ...
2
votes
0answers
196 views

Is this approach to the combinatorics of knots well known?

I am teaching a course on knots for the first time, and this led me to play with an approach which I have not seen in the literature. I would be surprised if no one had used it before, so I am ...
2
votes
1answer
66 views

Boundary energy estimate of wave equations

Let $D$ be the unit disk in $\mathbb{R}^{n}$, we consider the $n$ dimension wave equation defined on $D$, $$\square u=F$$ where $\square=\partial_{t}^{2}-\triangle$ is the standard wave operator in ...
0
votes
0answers
112 views

Reference Request: Category of explicit maps between primitive recursive sets?

[Edited] Let $\mathsf{PR}$ be the category defined as follows: Choose a specific presentation of Primitive Recursive Arithmetic, that is, with a specific set of terms for primitive recursive ...
0
votes
0answers
27 views

References for symmetric α-stable process (SSP) for $a>2$

Many properties of Brownian motion have been extended to SSP's for $0\leq \alpha\leq 2$ and so it is quite easy to find literature on them. However, I am currently studying the SSP for $\alpha>2$ ...
0
votes
0answers
35 views

Reference request: Wong-Zakai smooth approximation in probabilty for stochastic differential equations

I'm looking for a result of the form: Let $B_\epsilon$ denote a "natural" smooth $\epsilon$-approximation to a $n$-dimensional Brownian motion $B$ (e.g. by mollification or simply piecewise linear) ...
8
votes
0answers
310 views

Pairing of cohomology and homology Künneth formulas

Let $k$ be a field, and let $X$ and $Y$ be CW-complexes of finite type (although the question makes sense for $k$ a ring and for more general chain complexes of finitely generated free abelian ...
2
votes
2answers
425 views
+50

orbits of linear algebraic group $G({\Bbb Q}_p)$ acting on subgroups of ${\Bbb Q}_p^n$

Let $G\subseteq GL(n)$ be a linear algebraic group, and let $G({\Bbb Q}_p)\subseteq GL(V)$ act on a ${\Bbb Q}_p$-vector space V of finite dimension. Consider the action of $G$ on abelian subgroups ...
2
votes
2answers
118 views

Upper bounds on the edge clique cover number on special graph classes

An edge clique cover of an undirected graph $G$ is a set of cliques of $G$ such that every edge of $G$ is an edge in at least one clique in the set. The edge clique cover number $\theta(G)$ is the ...
4
votes
2answers
278 views

Concise mathematical definition of the fusion product on the Verlinde ring?

The Verlinde ring of a (let us say) simply connected simple compact Lie group has as underlying additive group the Grothendieck group of representations of the central extension $\widehat{LG}$ of the ...
20
votes
1answer
646 views

fake $S^{2k}\times S^{2k}$

Let $X$ be a fixed closed manifold,$S(X)$ the structure set and $Aut(X)$ the group of self homotopy equivalence of $X$. surgery theory tells us that $\mathcal{M}(X):=S(X)/Aut(X)$ is in bijection ...
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0answers
151 views

Property theories

Property theory is, as I have understood it, first of all characterized by an attempt to approach naive comprehension type-freely and without committing to extensionality. There is e.g. the work of ...
-4
votes
1answer
58 views

Resources to learn about hypergraphs [closed]

I am working on a project that is based on hyper graphs. Is there any resource that I could refer to understand the basics properties of hyper graphs ?
1
vote
1answer
61 views

What is the fractional derivative smoothness of functions from the Zygmund class?

Let $\Lambda([0,1])$ be the Zygmund class of continuous on $[0,1]$ functions for which $$\sup h^{-1}|f(x+2h)-2f(x+h)+f(x)|<\infty.$$ What would be the exact smoothness class for the fractional ...
1
vote
1answer
70 views

Explicit deformations of pseudo representations

Let $G$ be a group (which I will be glad to consider to be the absolute Galois group of a $p$-adic field, and so satisfies Mazur's finiteness condition which appears in his paper Deforming Galois ...