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Séminaire Géométrie et théorie des modèles

Horaires : Le vendredi 13 mai 2016, 16h

Lieu : Salle W, ENS

Wave front sets of distributions in non-archimedean analysis

Michel Raibaut (Chambéry)

In 1969, Sato and Hörmander introduced the notion of wave front set of a distribution in the real context. This concept gives a better understanding of operations on distributions such as product or pullback and it plays an important role in the theory of partial differential equations. In 1981, Howe introduced a notion of wave front set for some Lie group representations and in 1985, Heifetz gave an analogous version in the p-adic context. In this talk, in the t-adic context in characteristic zero, using Cluckers-Loeser motivic integration we will present analogous constructions of test functions, distributions and wave front sets. In particular, we will explain how definability can be used as a substitute for topological compactness of the sphere in the real and p-adic contexts to obtain finiteness. This a joint work with R. Cluckers, and F. Loeser.


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