Jean Gillibert (Université de Caen)
jean.gillibert@math.unicaen.fr
We first introduce the ideas of Hopf-Galois theory as an attempt to taming wild extensions with Hopf algebras, in connection with the problems of Galois module structure in arithmetic. Then, following the works of M. Taylor and G. Pappas, we explain how one obtains, from an elliptic curve having everywhere good reduction, a family of algebras with trivial Galois module structure. Finally we discuss on a possible generalisation to the semi-stable case.