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Ramification groups in Artin-Schreier-Witt extensions

Lara Thomas — 2005

Journal de Théorie des Nombres de Bordeaux

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...

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