A refinement of the local class field theory of Serre and Hazewinkel

Abstract

We give a refinement of the local class field theory of Serre and Hazewinkel. This refinement allows the theory to treat extensions that are not necessarily totally ramified. Such a refinement was obtained and used in the authors' paper on Fontaine's property (Pm), where the explanation had to be rather brief. In this paper, we give a complete account, from necessary knowledge of an appropriate Grothendieck site to the details of the proof. We start by reviewing the local class field theory of Serre and Hazewinkel.

29 pages, final version to appear in Algebraic Number Theory and Related Topics 2010, 163--191, RIMS Kôkyûroku Bessatsu, B32, Res. Inst. Math. Sci. (RIMS), Kyoto, 2012

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