A partial analog of the integrability theorem for distributions on p-adic spaces and applications

Abstract

Let X be a smooth real algebraic variety. Let ξ be a distribution on it. One can define the singular support of ξ to be the singular support of the DX-module generated by ξ (sometimes it is also called the characteristic variety). A powerful property of the singular support is that it is a coisotropic subvariety of T*X. This is the integrability theorem (see [KKS, Mal, Gab]). This theorem turned out to be useful in representation theory of real reductive groups (see, e.g., [AG4, AS, Say]).