Ramification groups in Artin-Schreier-Witt extensions. (English) Zbl 1207.11109

Summary: 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 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.


11S15 Ramification and extension theory
11S31 Class field theory; \(p\)-adic formal groups
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