#### Vol. 10, No. 10, 2016

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Constructible isocrystals

### Bernard Le Stum

Vol. 10 (2016), No. 10, 2121–2152
##### 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 $\mathsc{D}$-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
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