Arithmetic and Differential Swan Conductors of rank one representations with finite local monodromy - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue American Journal of Mathematics Année : 2009

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

Résumé

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.

Dates et versions

hal-00803817 , version 1 (22-03-2013)

Identifiants

Citer

Bruno Chiarellotto, Andrea Pulita. Arithmetic and Differential Swan Conductors of rank one representations with finite local monodromy. American Journal of Mathematics, 2009, Vol.131, p.1743-1794. ⟨10.1353/ajm.0.0083⟩. ⟨hal-00803817⟩
44 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More