Arithmetic D-modules over algebraic varieties of characteristic p>0

TL;DR

This paper develops a $p$-adic formalism for Grothendieck's six operations on realizable schemes over fields of characteristic p>0, extending Berthelot’s theory of arithmetic D-modules to a broader setting.

Contribution

It introduces a new $p$-adic formalism for Grothendieck's six operations applicable to realizable schemes over characteristic p>0, broadening the scope of Berthelot’s arithmetic D-modules.

Findings

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

Extended Berthelot's theory to non-perfect fields of characteristic p>0.

Provided tools for further research in arithmetic geometry over positive characteristic fields.

Abstract

Let $k$ be a field of characteristic $p>0$ not necessarily perfect. Using Berthelot's theory of arithmetic $\mathcal{D}$-modules, we construct a $p$-adic formalism of Grothendieck's six operations for realizable $k$-schemes of finite type.