Related papers: Galois Automorphisms and Classical Groups

Let S be a compact orientable surface with genus g and n boundary components d_1,...,d_n. Let b = (b_1, ..., b_n) where b_n lies in [-2,2]. Then the mapping class group of S acts on the relative SU(2)-character variety X comprising…

The aim of this article is to explore global and local properties of finite groups whose integral group rings have only trivial central units, so-called cut groups. For such a group we study actions of Galois groups on its character table…

We characterize the groups isomorphic to full automorphism groups of ordered abelian groups. The result will follow from classical theorems on ordered groups adding an argument from proofs used to realize rings as endomorphism rings of…

We prove that there are infinitely many finite simple groups of symplectic Lie type, of any specified characteristic and rank, which appear as Galois groups over the field of rational numbers. This generalizes a result of Wiese, which…

In this paper, we describe Galois covers of algebraic curves and their families by using local systems associated to push-forward of sheaves by the structure morphism. More precisely, if $f:C\to Y$, we consider the sheaves $f_*(\C)$. The…

This article is the first part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. In this first part, we determine the smallest field over which the…

We are given a finite group $H$, an automorphism $\tau$ of $H$ of order $r$, a Galois extension $L/K$ of fields of characteristic zero with cyclic Galois group $\langle\sigma\rangle$ of order $r$, and an absolutely irreducible…

We give an accessible and modern description of the automorphisms of a finite abelian group $G$. Included is an explicit formula for the cardinality of $Aut(G)$.

We classify non symplectic prime order automorphisms and all finite order symplectic automorphism groups of generalised Kummer fourfolds using lattice theory and recent results on ample cones and monodromy groups. We study various geometric…

We prove a Galois correspondence theorem for groupoids acting orthogonally and partially on commutative rings. We also consider partial actions that are not orthogonal, presenting two correspondences in this case: one for strongly Galois…

We prove new automorphy lifting theorems for residually reducible Galois representations of unitary type in which the residual representation is permitted to have an arbitrary number of irreducible constituents.

We establish a quantum Galois correspondence for compact Lie groups of automorphisms acting on a simple vertex operator algebra.

We study the residual monodromy representations associated to the Dwork family in characteristic two. Various applications involving 2-adic and mod 2 Galois representations are discussed. Combining the author's previous work with Tsuzuki…

We give a complete classification of finite groups acting symplectically on supersingular K3 surfaces of Artin invariant one. Using work of Dolgachev and Keum, this provides the full classification of tame finite symplectic automorphism…

In the present paper, we study the outer automorphism groups of the absolute Galois groups of 2-adic local fields from the point of view of anabelian geometry. Let us recall that it is well-known that the natural homomorphism from the…

We prove that the automorphism groups of simple polarized abelian varieties of odd prime dimension over finite fields are cyclic, and give a complete list of finite groups that can be realized as such automorphism groups.

We give a uniform construction of irreducible polynomial representations of all classical groups, including spin groups, using semistandard domino tableaux. We also give an explicit decomposition of the homogeneous coordinate ring of the…

In this paper we determine automorphism groups of cyclic algebraic curves defined over finite fields of any characteristic.

Let O be a complete discrete valuation domain with finite residue field. In this paper we describe the irreducible representations of the groups Aut(M) for any finite O-module M of rank two. The main emphasis is on the interaction between…

In this paper, we study extra-twists for automorphic representations of $\mathrm{GL}_n$ and use them to give a precise description of the image of the Galois representations associated with regular algebraic cuspidal automorphic…