Arithmetic D-modules on locally noetherian formal schemes

TL;DR

This paper extends Berthelot's theory of arithmetic D-modules to broader morphisms and constructs a new category of convergent isocrystals, demonstrating Frobenius pullback as an auto-equivalence, thus broadening the theory's applicability.

Contribution

It generalizes the theory of arithmetic D-modules to non-finite type morphisms and provides a new construction of convergent isocrystals with Frobenius auto-equivalence.

Findings

Extended arithmetic D-modules to non-finite type morphisms

Constructed a new category of convergent isocrystals

Proved Frobenius pullback is an auto-equivalence

Abstract

We extend Berthelot's theory of arithmetic D-modules to a class of morphisms that are not necessarily of finite type. As an application we give a new construction of the category of convergent isocrystals on a separated scheme of finite type over a field, and show that the pullback by Frobenius is an auto-equivalence. This extends results of Berthelot that were proven in the smooth case.