Galois scaffolds for cyclic $$p^n$$-extensions in characteristic p

Abstract

Let K be a local field of characteristic p > 0 with perfect residue field and let G be a finite p-group. In this paper we use Saltman's construction of a generic G-extension of rings of characteristic p to construct totally ramified G-extensions L/K that have Galois scaffolds. We specialize this construction to produce Gextensions L/K such that the ring of integers O L is free of rank 1 over its associated order A 0 , and extensions such that A 0 is a Hopf order in the group ring K[G].