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arXiv · 0711.0701

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

Bruno Chiarellotto·Andrea Pulita
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Abstract

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 $D^†(V)$ 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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Bruno Chiarellotto, Andrea Pulita. 2008-08-04. Arithmetic and Differential Swan Conductors of rank one representations with finite local monodromy. https://arxiv.org/abs/0711.0701

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