Constructible isocrystals

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 $\mathcal{D}$-modules. We prove here that a constructible isocrystal is completely determined by any of its geometric realizations.