Ramification of local fields with imperfect residue fields I

Abstract

Let K be a complete discrete valuation field, and let G be the Galois group of a separable closure Ω. Classically the ramification filtration of G is defined in the case where the residue field of K is perfect ([5], Chapter IV). In this paper, we define without any assumption on the residue field, two ramification filtrations of G and study some of their properties. Our first filtration, (G)a∈Q≥0 , satisfies the following properties:

Cite this paper

@inproceedings{Saito2009RamificationOL, title={Ramification of local fields with imperfect residue fields I}, author={Takeshi Saito}, year={2009} }