Arithmetic $\mathcal{D}$-modules over Laurent series fields: absolute case

TL;DR

This paper develops a $p$-adic formalism for Grothendieck's six operations within Berthelot's theory of arithmetic $ ext{D}$-modules over Laurent series fields, specifically over $ ext{Spec} k[[t]]$ for a perfect field $k$ of characteristic $p>0$.

Contribution

It introduces a new $p$-adic formalism of Grothendieck's six operations for arithmetic $ ext{D}$-modules over Laurent series fields, extending Berthelot's framework.

Findings

Constructs a $p$-adic formalism for Grothendieck's six operations

Applies to quasi-projective schemes over $ ext{Spec} k[[t]]$

Enhances the theory of arithmetic $ ext{D}$-modules in positive characteristic

Abstract

Let $k$ be a perfect field of characteristic $p>0$. Within Berthelot's theory of arithmetic $\mathcal{D}$-modules, we construct a $p$-adic formalism of Grothendieck's six operations for quasi-projective schemes over $\mathrm{Spec} k[[t]]$.