Kashiwara's theorem for twisted arithmetic differential operators

TL;DR

This paper extends Kashiwara's theorem to twisted arithmetic differential operators on smooth p-adic formal schemes and applies it to construct modules for crystalline distribution algebras of reductive groups.

Contribution

It introduces a twisted version of Kashiwara's theorem for arithmetic differential operators and uses it to build modules for crystalline distribution algebras.

Findings

Established Kashiwara's theorem for twisted sheaves of arithmetic differential operators.

Constructed simple modules for crystalline distribution algebras of reductive groups.

Provided a new approach to crystalline localisation in the p-adic setting.

Abstract

We establish a version of Kashiwara's theorem for twisted sheaves of Berthelot's arithmetic differential operators for a closed immersion between smooth p-adic formal schemes. As an application, we construct simple modules for crystalline distribution algebras of reductive groups using the twisted version of the crystalline localisation theorem.