Galois algebras and their homomorphisms.
Galois characters associated to formal -modules
Galois Covers and the Hilbert-Grunwald Property
Our main result combines three topics: it contains a Grunwald-Wang type conclusion, a version of Hilbert’s irreducibility theorem and a -adic form à la Harbater, but with good reduction, of the Regular Inverse Galois Problem. As a consequence we obtain a statement that questions the RIGP over . The general strategy is to study and exploit the good reduction of certain twisted models of the covers and of the associated moduli spaces.
Galois covers between surfaces
We give a classification of finite group actions on a surface giving rise to quotients, from the point of view of their fixed points. It is shown that except two cases, each such group gives rise to a unique type of fixed point set.
Galois covers of over with prescribed local or global behavior by specialization
This paper considers some refined versions of the Inverse Galois Problem. We study the local or global behavior of rational specializations of some finite Galois covers of .
Galois generators and the subspace theorem.
Galois groups of exponent two and the Brumer-Stark conjecture.
Galois module structure of abelian extensions.
Galois module structure of integers of relative abelian extensions.
Galois module structure of rings of integers
Let be a Galois extension of number fields with Gal and with property that the divisors of are non-ramified in . We denote the ring of integers of by and we study as a -module. In particular we show that the fourth power of the (locally free) class of is the trivial class. To obtain this result we use Fröhlich’s description of class groups of modules and his representative for the class of , together with new determinantal congruences for cyclic group rings and corresponding congruences...
Galois modules and embedding problems.
Galois representations, embedding problems and modular forms.
To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations...
Galois towers over non-prime finite fields
We construct Galois towers with good asymptotic properties over any non-prime finite field ; that is, we construct sequences of function fields = (N₁ ⊂ N₂ ⊂ ⋯) over of increasing genus, such that all the extensions are Galois extensions and the number of rational places of these function fields grows linearly with the genus. The limits of the towers satisfy the same lower bounds as the best currently known lower bounds for the Ihara constant for non-prime finite fields. Towers with these properties...
Galoismoduln mit Hasse-Prinzip.
Genus zero translates of three point ramified Galois extensions.
GLn (q) as Galois group over the rationals.
Greenberg's conjecture and cyclotomic towers
Group laws and rings with normal bases.
Groupe de Galois de la p-extension abélienne p-ramifiée maximale d'un corps de nombres.
Groupe des unités pour des extensions diédrales complexes de degré sur
Le but de cet article est de montrer qu’un ensemble quelconque de quatre racines des polynômes quintiques exhibés par . Darmon forme sous certaines conditions un système fondamental d’unités de la fermeture normale du corps où .