Syntomic cohomology and p-adic regulators for varieties over p-adic fields.

Abstract : We show that the logarithmic version of the syntomic cohomology of Fontaine and Messing for semistable varieties over p-adic rings extends uniquely to a cohomology theory for varieties over p-adic fields that satisfies h-descent. This new cohomology-syntomic cohomology-is a Bloch-Ogus cohomology theory, admits period map tó etale cohomology, and has a syntomic descent spectral sequence (from an algebraic closure of the given field to the field itself) that is compatible with the Hochschild-Serre spectral sequence on thé etale side and is related to the Bloch-Kato exponential map. In relative dimension zero we recover the potentially semistable Selmer groups and, as an application, we prove that Soulé's ´ etale regulators land in the potentially semistable Selmer groups. Our construction of syntomic cohomology is based on new ideas and techniques developed by Beilinson and Bhatt in their recent work on p-adic comparison theorems.
Type de document :
Article dans une revue
Algebra & Number Theory, 2016
Liste complète des métadonnées

Littérature citée [27 références]  Voir  Masquer  Télécharger

https://hal-ens-lyon.archives-ouvertes.fr/ensl-01420345
Contributeur : Wieslawa Niziol <>
Soumis le : mardi 20 décembre 2016 - 14:36:22
Dernière modification le : jeudi 11 janvier 2018 - 02:03:24
Document(s) archivé(s) le : mardi 21 mars 2017 - 03:10:40

Fichier

lastone.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : ensl-01420345, version 1

Collections

Citation

Jan Nekovar, Wieslawa Niziol. Syntomic cohomology and p-adic regulators for varieties over p-adic fields.. Algebra & Number Theory, 2016. 〈ensl-01420345〉

Partager

Métriques

Consultations de la notice

57

Téléchargements de fichiers

25