Constructible isocrystals

Le Stum, Bernard

doi:10.2140/ant.2016.10.2121

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Constructible isocrystals

Bernard Le Stum

Vol. 10 (2016), No. 10, 2121–2152

DOI: 10.2140/ant.2016.10.2121

Abstract

We introduce a new category of coefficients for $p$ -adic cohomology called constructible isocrystals. Conjecturally, the category of constructible isocrystals endowed with a Frobenius structure is equivalent to the category of perverse holonomic arithmetic $D$ -modules. We prove here that a constructible isocrystal is completely determined by any of its geometric realizations.

Keywords

constructible isocrystal, overconvergent isocrystal, rigid cohomology, $p$-adic cohomology, module with connection

Mathematical Subject Classification 2010

Primary: 14F30

Milestones

Received: 26 January 2016

Revised: 5 September 2016

Accepted: 12 November 2016

Published: 9 December 2016

Authors

Bernard Le Stum
Institut de Recherche Mathematique (IRMAR) Universite de Rennes I 35042 Rennes France

Vol. 10, No. 10, 2016