On Involutivity of p-Support

Abstract

The p-support of a holonomic D-module was introduced by Kontsevich. Thomas Bitoun in his PhD thesis proved several properties of p-support conjectured by Kontsevich. In this note, we give an alternative proof for involutivity by reducing it to a slight extension of Gabber's theorem on the integrability of the characteristic variety. For the benefit of the reader, we review how this extension follows from Kaledin's proof of Gabber's theorem.