  The class-invariant homomorphism allows one to measure the Galois module
structure of torsors--under a finite flat group scheme--which lie in the image
of a coboundary map associated to an exact sequence. It has been introduced
first by Martin Taylor (the exact sequence being given by an isogeny between
abelian schemes). We begin by giving general properties of this homomorphism,
then we pursue its study in the case when the exact sequence is given by the
multiplication by $n$ on an extension of an abelian scheme by a torus.
