2018/10/24 by Raibaut, Michel
#Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1810.10567
The concept of wave front set was introduced in 1969-1970 by M. Sato in the hyperfunctions context and by L. Hörmander in the \mathcal C∞ context. Howe used the theory of wave front sets in the study of Lie groups representations. Heifetz defined a notion of wave front set for distributions in the p-adic setting and used it to study some representations of p-adic Lie groups. In this article, we work in the k((t))-setting with k a characteristic zero field. In that setting, balls are no longer compact but working in a definable context provides good substitutes for finiteness and compactness properties. We develop a notion of definable distributions in the motivic integration framework of Cluckers--Loeser for which we define notions of singular support and Λ-wave front sets (relative to some multiplicative subgroups Λ of the valued field) and we investigate their behaviour under natural operations like pull-back, tensor product, and products of distributions.