Arithmetic and Differential Swan Conductors of rank one representations with finite local monodromy

Details Arithmetic and Differential Swan Conductors of rank one representations with finite local monodromy Arithmetic and Differential Swan Conductors of rank one representations with finite local monodromy

2007-11-05

arxiv.org/abs/0711.0701v2

Mathematics

Number Theory

38 pages

Scientific paper

We consider a complete discrete valuation field of characteristic p, with possibly non perfect residue field. Let V be a rank one continuous representation with finite local monodromy of its absolute Galois group. We will prove that the Arithmetic Swan conductor of V (defined after Kato in [Kat89] which fits in the more general theory of [AS02] and [AS06]) coincides with the Differential Swan conductor of the associated differential module $D^{\dag}(V)$ defined by Kedlaya in [Ked]. This construction is a generalization to the non perfect residue case of the Fontaine's formalism as presented in [Tsu98a]. Our method of proof will allow us to give a new interpretation of the Refined Swan Conductor.

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