We consider a complete discrete valuation field of characteristic p, with possibly nonperfect residue field. Let V be a rank one continuous representation of its absolute Galois group with finite local monodromy. we will prove that the arithmetic Swan conductor of V (defined after K. Kato, which fits in the more general theory of Abbes-Saito) coincides with the differential Swan conductor of the associated differential module D(dagger)(V) defined by K. Kedlaya. This construction is a generalization to the nonperfect residue case of the Fontaine's formalism as presented in the work of N. Tsuzuki. Our method of proof will allow us to give a new interpretation of the refined Swan conductor.

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

CHIARELLOTTO, BRUNO;
2009

Abstract

We consider a complete discrete valuation field of characteristic p, with possibly nonperfect residue field. Let V be a rank one continuous representation of its absolute Galois group with finite local monodromy. we will prove that the arithmetic Swan conductor of V (defined after K. Kato, which fits in the more general theory of Abbes-Saito) coincides with the differential Swan conductor of the associated differential module D(dagger)(V) defined by K. Kedlaya. This construction is a generalization to the nonperfect residue case of the Fontaine's formalism as presented in the work of N. Tsuzuki. Our method of proof will allow us to give a new interpretation of the refined Swan conductor.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/2376690
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 9
social impact