Fields generated by linear combinations of roots of unity, II.
Finitude de tours et -tours -ramifiées modérées, -décomposées
Soit un corps de nombres et soient et deux ensembles finis de places de ; on peut définir la tour de Hilbert de , -ramifiée modérée, -décomposée. Ceci permet d’obtenir, par exemple, la notion de tour de Hilbert au sens classique et de tour de Hilbert au sens restreint. On donne alors d’une part, un critère de finitude de cette nouvelle tour, critère construit à partir d’un résultat d’Odlyzko, puis d’autre part deux critères de non-finitude, le premier étant une conséquence d’un résultat...
Fonctions L d'Artin
Formal-reelle Körper mit streng-auflösbarer absoluter Galoisgruppe.
Freie Produktzerlegungen von Galoisgruppen und Iwasawa-Invarianten für p-Erweiterungen von ...
Frobenius groups and integral bases.
Functoriality and the Inverse Galois problem II: groups of type and
This paper contains an application of Langlands’ functoriality principle to the following classical problem: which finite groups, in particular which simple groups appear as Galois groups over ? Let be a prime and a positive integer. We show that that the finite simple groups of Lie type if and appear as Galois groups over , for some divisible by . In particular, for each of the two Lie types and fixed we construct infinitely many Galois groups but we do not have a precise control...
Fundamental units for orders in certain cubic number fields.
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...