$F^e$-modules with applications to $D$-modules

TL;DR

This paper extends the theory of $F^e$-modules to analyze $D$-modules, providing new insights and tools to address conjectures in mixed characteristic settings.

Contribution

It introduces an extended $F^e$-module framework and applies it to study $D$-submodules, advancing understanding of $F$-module duality and conjectures in mixed characteristic.

Findings

Extended $F^e$-module theory developed

Results on Matlis duals of $F$-finite modules generalized

Progress made on Lyubeznik-Yildirim conjecture in mixed characteristic

Abstract

Using a theory of $F^e$-modules (a natural extension of Lyubeznik's $F$-module theory), we extend results on Matlis dual of $F$-finite $F$-modules to $D$-submodules of $F^e$-finite $F^e$-modules and apply these results to address the Lyubeznik-Yildirim conjecture in mixed characteristic.