Logarithmic $p$-bases and arithmetical differential modules

TL;DR

This paper introduces a new concept called log p-smoothness, which generalizes existing notions, and extends Berthelot's construction of arithmetic D-modules within this broader framework.

Contribution

It defines log p-smoothness, a weaker condition than log-smoothness and local p-bases, and extends the theory of arithmetic D-modules accordingly.

Findings

Introduction of log p-smoothness concept

Extension of Berthelot's arithmetic D-modules construction

Analysis of properties under the new framework

Abstract

We introduce the notion of log $p$-smoothness which weakens that of log-smoothness and that of having locally $p$-bases. We extend Berthelot's construction of arithmetic $D$-modules and some properties in this context.