相关论文: Finite groups acting on coherent sheaves and Galoi…

For an arbitrary 5-fold ramified covering between compact Riemann surfaces, every possible Galois closure is determined in terms of the ramification data of the map; namely, the ramification divisor of the covering map. Since the group that…

Let $E$ be a primarily quasilocal field, $M/E$ a finite Galois extension and $D$ a central division $E$-algebra of index divisible by $[M\colon E]$. In addition to the main result of Part I, this part of the paper shows that if the Galois…

Let $k$ be an algebraically closed field of characteristic $p\ge 0$. Let $G$ be an affine group scheme over $k$. We classify the indecomposable exact module categories over the rigid tensor category $\text{Coh}_f(G)$ of coherent sheaves of…

Finite \'etale covers of a connected scheme $X$ are parametrised by the \'etale fundamental group via the monodromy correspondence. This was generalised to an exodromy correspondence for constructible sheaves, first in the topological…

In this paper I explore the structure of the fields of definition of Galois branched covers of the projective line over \bar Q. The first main result states that every mere cover model has a unique minimal field of definition where its…

For any finite group G and integer i, let $\mathcal{H}^i(G)$ be the set of all the isomorphism classes of the Galois cohomology groups $\hat{H}^i(K/k,E_K)$, where K/k runs over all the unramified G-extension of number fields and E_K denotes…

Let $G$ be a finite classical group of Lie type of rank $\ell$, defined over a field of characteristic $p>2$. In this work, we classify the irreducible representations of $G$ whose dimensions are bounded by a constant proportional to…

We show that the Galois group $Gal(\bar{\Q} /\Q)$ operates faithfully on the set of connected components of the moduli spaces of surfaces of general type, and also that for each element $\sigma \in Gal(\bar{\Q} /\Q)$ different from the…

For many finite groups, the Inverse Galois Problem can be approached through modular/automorphic Galois representations. This is a report explaining the basic strategy, ideas and methods behind some recent results. It focusses mostly on the…

Given a subgroup H of a finite group G, we begin a systematic study of the partial representations of G that restrict to global representations of H. After adapting several results from [DEP00] (which correspond to the case where H is…

The main purpose of this paper is to describe the abelian part $\mathcal G^{ab}_{K}$ of the absolute Galois group of a global function field $K$ as pro-finite group. We will show that the characteristic $p$ of $K$ and the non $p$-part of…

Given an object over the algebraic closure Qbar of Q, there is often no reason for invariants of the corresponding holomorphic object to be preserved by the absolute Galois group Gal(Qbar/Q), and in general this is not true, although it is…

This paper continues the study of certain two-dimensional Galois representations attached to modular forms (mod p) via a construction due to Deligne. In particular, we prove a criterion for determining when the representation is split when…

We study integral points on varieties with infinite \'etale fundamental groups. More precisely, for a number field $F$ and $X/F$ a smooth projective variety, we prove that for any geometrically Galois cover $\varphi\colon Y \to X$ of degree…

An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…

Let $f: X \to Y$ be a regular covering of a surface $Y$ of finite type with nonempty boundary, with finitely-generated (possibly infinite) deck group $G$. We give necessary and sufficient conditions for an integral homology class on $X$ to…

We study the arithmetic of curves and Jacobians endowed with the action of a finite group $G$. This includes a study of the basic properties, as $G$-modules, of their $\ell$-adic representations, Selmer groups, rational points and…

This paper proves that if $E$ is a field, such that the Galois group $\mathcal{G}(E(p)/E)$ of the maximal $p$-extension $E(p)/E$ is a Demushkin group of finite rank $r(p)_{E} \ge 3$, for some prime number $p$, then $\mathcal{G}(E(p)/E)$…

Past studies of the Brauer group of a scheme tells us the importance of the interrelationship among Brauer groups of its finite \'etale coverings. In this paper, we consider these groups simultaneously, and construct an integrated object…

In this note I introduce a new approach to (or rather a new language for) representation theory of groups. Namely, I propose to consider a (complex) representation of a group $G$ as a sheaf on some geometric object (a stack). This point of…