Ramification groups in Artin-Schreier-Witt extensions

Abstract

Let K be a local field of characteristic p>0. The aim of this paper is to describe the ramification groups for the pro-p abelian extensions over K with regards to the Artin-Schreier-Witt theory. We shall carry out this investigation entirely in the usual framework of local class field theory. This leads to a certain non-degenerate pairing that we shall define in detail, generalizing in this way the Schmid formula to Witt vectors of length n. Along the way, we recover a result of Brylinski but with a different proof which is more explicit and requires less technical machinery. A first attempt is finally made to extend these computations to the case where the perfect field of K is merely perfect.