Abstract :
We investigate the Galois module structure of wildly ramified extensions. We are interested in particular in the second invariant of an extension of number fields defined by Chinburg via the canonical class of the extension and lying in the locally free class group. We show that in QueyrutʹsS-class group, whereSis a (finite) set of primes, the image of Chinburgʹs invariant equals the stable isomorphism class of the ring of integers and thus extend Chinburgʹs result for tame extensions.
