Galois module structure

Galois module structure deals with the construction of algebraic invariants from a Galois extension of number fields with group G. Typically these invariants lie in the class-group of some group-ring of G or of a related order. These class-groups have "Hom-descriptions" in terms of idèlic-valued functions on the complex representations of G. Following a theme pioneered by A. Frölich, T. Chinburg constructed several invariants whose Hom-descriptions are (conjecturally) given in terms of Artin root numbers. For a tame extension, the second Chinburg invariant is given by the ring of integers, and