Full faithfulness for overconvergent F-de Rham–Witt connections

Abstract

Let X be a smooth variety over a perfect field of characteristic p > 0. We define overconvergent F-de Rham-Witt connections as an analogue for F-crystals over proper schemes. We prove that the forgetful functor from the category of overconvergent F-de Rham-Witt connections to the category of convergent F-de Rham-Witt connections is fully faithful. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.