Lagrangianity for log extendable overconvergent F-isocrystals

In the framework of Berthelot’s theory of arithmetic D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {D}}$$\end{document}-modules, we prove that Berthelot’s characteristic variety associated with a holonomic D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {D}}$$\end{document}-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.