  We define here an analogue, for the N\'eron model of a semi-stable abelian
variety defined over a number field, of M. J. Taylor's class-invariant
homomorphism (defined for abelian schemes). Then we extend an annulation result
(in the case of an elliptic curve), and an injectivity result regarding an
arakelovian version of this homomorphism. This is the sequel to the paper
"Invariants de classes : le cas semi-stable".
