Full faithfulness for overconvergent F-de Rham-Witt connections

TL;DR

This paper establishes that the functor forgetting overconvergent F-de Rham-Witt connections to convergent ones is fully faithful, extending Kedlaya's ideas to a new setting involving overconvergent F-crystals.

Contribution

It introduces overconvergent F-de Rham-Witt connections and proves the full faithfulness of the forgetful functor, generalizing Kedlaya's results to this context.

Findings

The forgetful functor is fully faithful.

Overconvergent F-de Rham-Witt connections are well-defined analogues of F-crystals.

The proof adapts Kedlaya's approach to a new setting.

Abstract

Let X be a smooth variety over a perfect field of characteristic p>0. In this small note 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. The argument is an analogue of a discussion by Kedlaya on full faithfulness of overconvergent F-isocrystals.}