  Let $X$ be a fine and saturated log scheme, and let $G$ be a commutative
finite flat group scheme over the underlying scheme of $X$. If $G$-torsors for
the fppf topology can be thought of as being unramified objects by nature, then
$G$-torsors for the log flat topology allow us to consider tame ramification.
Using the results of Kato, we define a concept of Galois structure for these
torsors, then we generalize the author's previous constructions
(class-invariant homomorphism for semi-stable abelian varieties) in this new
setting, thus dropping some restrictions.
