Related papers: On certain permutation groups and sums of two squa…

We prove that, on average, elliptic curves over Q have finitely many primes p for which they possess a p-adic point of order p. We include a discussion of applications to companion forms and the deformation theory of Galois representations.

The use of double groupoids and their associated double Lie algebroids and characteristic distributions is proposed for the description and analysis of continuous media that carry two different constitutive or geometric structures. Various…

We present the generating function for the numbers of isomorphism classes of coverings of the two-dimensional sphere by the genus $g$ compact oriented surface not ramified outside of a given set of $m+1$ points in the target, fixed…

We continue our study of the reduction of PEL Shimura varieties with parahoric level structure at primes p at which the group that defines the Shimura variety ramifies. We describe "good" $p$-adic integral models of these Shimura varieties…

Consider an elliptic curve $E$ over a number field $K$. Suppose that $E$ has supersingular reduction at some prime $\mathfrak{p}$ of $K$ lying above the rational prime $p$. We completely classify the valuations of the $p^n$-torsion points…

We study some integral model of P.E.L. Shimura varieties of type A for ramified primes. Precisely, we look at the Pappas-Rapoport model (or splitting model) of some unitary Shimura varieties for which there is ramification in the degree 2…

Conditions, related to the so-called bending problem are considered for hypersurfaces of a pseudo-Euclidean space. Corresponding theorems are proved.

We prove a simultaneous generalization of the classical Riemann-Hurwitz and Plucker formulas, addressing the total inflection of a morphism from a (smooth, projective) curve to an arbitrary (smooth, projective) higher-dimensional variety.…

The random permutation is the Fra\"iss\'e limit of the class of finite structures with two linear orders. Answering a problem stated by Peter Cameron in 2002, we use a recent Ramsey-theoretic technique to show that there exist precisely 39…

Let $G$ be a split reductive group with $\dim Z(G) \leq 1$. We show that for any prime $p$ that is large enough relative to $G$, there is a finitely ramified Galois representation $\rho \colon \Gamma_{\mathbb Q} \to G(\mathbb Z_p)$ with…

Consider a finite, regular cover $Y\to X$ of finite graphs, with associated deck group $G$. We relate the topology of the cover to the structure of $H_1(Y;\mathbb{C})$ as a $G$-representation. A central object in this study is the {\em…

We prove a topological version of the section conjecture for the profinite completion of the fundamental group of finite CW-complexes equipped with the action of a group of prime order $p$ whose $p$-torsion cohomology can be killed by…

We prove multiplier theorems on rank one noncompact symmetric spaces which improve aspects of existing results. A common theme of our main results is that we partially drop specific assumptions on the multiplier function such as a…

We compute the inertia group of the compositum of wildly ramified Galois covers. It is used to show that even the $p$-part of the inertia group of a Galois cover of $\PP^1$ branched only at infinity can be reduced if there is a jump in the…

For any closed oriented surface F of genus at least three, we prove the existence of foliated F-bundles over surfaces such that the signatures of the total spaces are non-zero. We can arrange that the total holonomy of the horizontal…

We study complex projective manifolds X that admit surjective endomorphisms f:X->X of degree at least two. In case f is etale, we prove structure theorems that describe X. In particular, a rather detailed description is given if X is a…

This is a first in a series of papers, devoted to the relation betwwen three-manifolds and number fields. The present paper studies first homology of finite coverings of a three-manifold with primary interest in the Thurston $b_1$…

Given a foliation $\mathcal{F}$ on $X$ and an embedding $X\subseteq Y$, is there a foliation on $Y$ extending $\mathcal{F}$? Using formal methods, we show that this question has an affirmative answer whenever the embedding is sufficiently…

Generalizations of Redfield's master theorem and superposition theorem are proved by using decomposition of the tensor product of several induced monomial representations of the symmetric group $S_d$ into transitive constituents. As direct…

This note presents two observations which have in common that they lie at the boundary of toric geometry. The first one because it concerns the deformation of affine toric varieties into non toric germs in order to understand how to avoid…