SYNTOMIC COMPLEXES AND p-ADIC NEARBY CYCLES - ENS de Lyon - École normale supérieure de Lyon Accéder directement au contenu
Article Dans Une Revue Inventiones Mathematicae Année : 2017

SYNTOMIC COMPLEXES AND p-ADIC NEARBY CYCLES

Résumé

We compute syntomic cohomology of semistable affinoids in terms of cohomology of (ϕ, Γ)-modules which, thanks to work of Fontaine-Herr, Andreatta-Iovita, and Kedlaya-Liu, is known to compute Galois cohomology of these affinoids. For a semistable scheme over a mixed characteristic local ring this implies a comparison isomorphism, up to some universal constants, between truncated sheaves of p-adic nearby cycles and syntomic cohomology sheaves. This generalizes the comparison results of Kato, Kurihara, and Tsuji for small Tate twists (where no constants are necessary) as well as the comparison result of Tsuji that holds over the algebraic closure of the field. As an application, we combine this local comparison isomorphism with the theory of finite dimensional Banach Spaces and finiteness ofétale ofétale cohomology of rigid analytic spaces proved by Scholze to prove a Semistable conjecture for formal schemes with semistable reduction.
Fichier principal
Vignette du fichier
logvanishing6.pdf (665.5 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

ensl-01420358 , version 1 (20-12-2016)

Identifiants

  • HAL Id : ensl-01420358 , version 1

Citer

Pierre Colmez, Wieslawa Niziol. SYNTOMIC COMPLEXES AND p-ADIC NEARBY CYCLES. Inventiones Mathematicae, 2017, 1, pp.1-108. ⟨ensl-01420358⟩
188 Consultations
243 Téléchargements

Partager

Gmail Facebook X LinkedIn More