Abstract : In this thesis we study the Galois structure of torsors under finite or quasi-finite flat group schemes. To this end, we use and generalize a homomorphism defined
by W. Waterhouse and the so-called class invariant homomorphism of M. J. Taylor.
In Chapter I, we develop functorial properties of these homomorphisms and apply them to generalize results of Taylor, Srivastav, Agboola and Pappas concerning
the kernel of the class invariant homomorphism to Abelian varieties with everywhere good reduction that are isogenous to a product of elliptic curves.
In Chapter II, we interpret the class invariant homomorphism in terms of 1-motives.
In Chapter III, we generalize the construction of the class invariant homomorphism to finite flat subgroups of semi-stable group schemes over an integral, normal and noetherian base whose general fiber is an Abelian variety. We also extend the results of Taylor,
Srivastav, Agboola and Pappas to this situation.
In Chapter IV, we discuss how the results of Chapter III can be generalized to the context of closed quasi-finite flat subgroup schemes when the base is a Dedekind scheme. We also generalize an arakelovian result of Agboola and Pappas to this situation.