Appears in collection : 2018 - T1 - WS2 - Model theory and valued fields

I will recall some concrete parts of the course on motivic integration given at the IHP by Halupczok, and use it to define distributions of C-exp class on p-adic spaces. I will then study the wave front sets of these distributions, and make a link with zero loci of functions of Cexp class which provides an answer to a recent question raised by Aizenbud and Drinfeld. This concerns joint work with Aizenbud, Gordon, Halupczok, Loeser, and Raibaut (in various combinations).