相关论文: On the arithmetic Galois covers of higher relative…

We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of…

We develop a computational framework for the statistical characterization of Galois characters with finite image, with application to characterizing Galois groups and establishing equivalence of characters of finite images of…

This article deals with the Galois representation attached to elliptic curves with an isogeny of prime degree over a number field. We first determine uniform criteria for the irreducibility of Galois representations attached to elliptic…

This note explores the consequences of Koenigsmann's model theoretic argument from the proof of the birational p-adic section conjecture for curves in the context of higher dimensional varieties over p-adic local fields.

In this note we study the associated adelic representation of a product of hyperelliptic Jacobians. We give a simple criterion that assures that this representation has maximal Galois image in a certain sense. As an application, we provide…

We develop a Galois theory for systems of linear difference equations with an action of an endomorphism {\sigma}. This provides a technique to test whether solutions of such systems satisfy {\sigma}-polynomial equations and, if yes, then…

The main purpose of this paper is to provide explicit computations of the fundamental group of several algebras. For this purpose, given a $k$-algebra $A$, we consider the category of all connected gradings of $A$ by a group $G$ and we…

Let $k$ be a commutative ring. We study the behaviour of coverings of $k$-categories through fibre products and find a criterion for a covering to be Galois or universal.

A strategy to address the inverse Galois problem over Q consists of exploiting the knowledge of Galois representations attached to certain automorphic forms. More precisely, if such forms are carefully chosen, they provide compatible…

This paper is concerned with difference equations on elliptic curves. We establish some general properties of the difference Galois groups of equations of order two, and give applications to the calculation of some difference Galois groups.…

We classify Galois objects for the dual of a group algebra of a finite group over an arbitrary field.

Given a pair of n-dimensional complex Galois representations over Q, we define their matching density to be the density, if it exists, of the set of places at which the traces of Frobenius of the two Galois representations are equal. We…

We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.

We introduce a dynamical analogue of the lifting problem for Galois covers of algebraic curves and find a negative solution for the collection of additive, separable polynomials over $\overline{\mathbb{F}}_p$. We also explicitly compute the…

In this paper we study the semi-stable reduction of Galois covers of degree p above semi-stable curves over a complete discrete valuation ring of inequal characteristics (0,p). We are also able to describe the Galois action on these covers…

We realize infinitely many covering groups $2.A_n$ (where $A_n$ is the alternating group) as the Galois group of everywhere unramified Galois extensions over infinitely many quadratic number fields. After several predecessor works…

In this paper we prove the existence of all higher logarithms as multivalued and ordinary Deligne cohomology classes.

We make explicit certain results around the Galois correspondence in the context of definable automorphism groups, and point out the relation to some recent papers dealing with the Galois theory of algebraic differential equations when the…

We survey some aspects of the theory of elliptic surfaces and give some results aimed at determining the Picard number of such a surface. For the surfaces considered, this will be equivalent to determining the Mordell-Weil rank of an…

An introductory review of algebraic classification of the Weyl tensor and algebraically special solutions in higher dimensions.