Lagrangianity for log extendable overconvergent $F$-isocrystals

TL;DR

This paper proves that the characteristic variety of certain arithmetic D-modules with Frobenius structure is pure-dimensional and Lagrangian, extending to log extendable overconvergent F-isocrystals within Berthelot's framework.

Contribution

It establishes the Lagrangianity of the characteristic variety for log extendable overconvergent F-isocrystals, advancing the understanding of their geometric properties.

Findings

Characteristic variety has pure dimension

Characteristic variety of log extendable overconvergent F-isocrystals is Lagrangian

Supports Berthelot's theory of arithmetic D-modules

Abstract

In the framework of Berthelot's theory of arithmetic $\mathcal{D}$-modules, we prove that Berthelot's characteristic variety associated with a holonomic $\mathcal{D}$-modules endowed with a Frobenius structure has pure dimension. As an application, we get the lagrangianity of the characteristic variety of a log extendable overconvergent $F$-isocrystal.