F-isocristaux unipotents

Abstract

We show that unipotent overconvergent isocrystals are algebraic and that the category of unipotent overconvergent isocrystals has a Frobenius automorphism. We also prove a structure theorem for unipotent overconvergent F-isocrystals over an open subset of the line, analogous to Dieudonne–Manin decomposition theorem for F-isocrystals.