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

Abstract: Using a theory of $F<sup>e$-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 $F<sup>e$-finite $F<sup>e$-modules and apply these results to address the Lyubeznik-Yildirim conjecture in mixed characteristic.