On the Galois theory of difference fields.
On the Galois Theory of function fields of one variable over number fields.
On the infinite fern of Galois representations of unitary type
Let be a CM number field, an odd prime totally split in , and let be the -adic analytic space parameterizing the isomorphism classes of -dimensional semisimple -adic representations of satisfying a selfduality condition “of type ”. We study an analogue of the infinite fern of Gouvêa-Mazur in this context and show that each irreducible component of the Zariski-closure of the modular points in has dimension at least . As important steps, and in any rank, we prove that any first order...
On the inverse problem of Galois theory.
The problem of the construction of number fields with Galois group over Q a given finite groups has made considerable progress in the recent years. The aim of this paper is to survey the current state of this problem, giving the most significant methods developed in connection with it.
On the nonexcellence of field extensions .
On the Nonflatness of Analytic Tensor Product.
On the number of real roots of a solvable polynomial
On the Pythagorean hull of Q.
The purpose of this paper is to prove that the Pythagorean hull of Q is the splitting field in R of a special set of rational polynomials.
On the semi-simplicity of Galois actions
On Torsion Points of Formal Groups over a Ring of Witt Vectors.
On trace forms of hilbertian fields.
On valued function fields II. Regular functions and elements with the uniqueness property.
Orderings under field extensions.
Ordre de transcendance sur
-extensions abéliennes
Parallélogrammes galoisiens infinis
Pfister's conjecture on quadratic Co-fields.
Plongeants d'extensions galoisiennes
Plongement d'une extension diédrale dans une extension diédrale ou quaternionienne
On utilise les méthodes de Neukirch et Poitou pour écrire les conditions locales et globales des problèmes de plongement. Le cas étudié ici est celui du plongement d’une extension diédrale dans une extension diédrale ou quaternionienne, le corps de base étant un corps de nombres.
Polynômes à groupe de Galois diédral
Soit un corps et une extension quadratique de . Étant donné un polynôme de à groupe de Galois cyclique, nous donnons une méthode pour construire un polynôme de à groupe de Galois diédral, à partir des racines de . Cette méthode est tout à fait explicite : nous donnons de nombreux exemples de polynômes à groupe de Galois diédral sur le corps .