Two interesting examples of $\mathcal{D}$-modules in characteristic $p>0$

TL;DR

This paper presents two specific examples of $ abla$-modules in characteristic p that resolve two open questions from prior research, demonstrating limitations in the current understanding of such modules.

Contribution

It introduces two explicit examples of $ abla$-modules in characteristic p that negatively answer open problems, advancing the theoretical understanding of $ abla$-modules.

Findings

Provided two explicit $ abla$-modules in characteristic p

Answered two open problems negatively

Contributed to the theoretical framework of $ abla$-modules

Abstract

We provide two examples of $\mathcal{D}$-modules in prime characteristic $p$ which answer two open problems in \cite{Lyubeznik} in the negative.