Constructible isocrystals

TL;DR

This paper introduces constructible isocrystals as a new coefficient category in p-adic cohomology, proving they are determined by geometric realizations and conjecturally equivalent to perverse holonomic arithmetic D-modules with Frobenius structure.

Contribution

It defines constructible isocrystals, establishes their determination by geometric realizations, and conjectures their equivalence to certain D-modules.

Findings

Constructible isocrystals are uniquely determined by their geometric realizations.

Conjecture: They are equivalent to perverse holonomic arithmetic D-modules with Frobenius.

The paper lays groundwork for a new coefficient theory in p-adic cohomology.

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.