Stickelberger elements for \(\mathbb Z^d_p\)-extensions of function fields (Q531776)

The authors show that Stickelberger elements associated to \(\mathbb Z_p^d\)-extensions over global fields of positive characteristic are generically irreducible in their Iwasawa algebras. Generic here means that whenever there is an irreducible Stickelberger element, then there is an open set, in the profinite topology, of a collection of appropriately related intermediate \(\mathbb Z_p^{d'}\)-extensions, each corresponding to an irreducible Stickelberger element.