On the commutativity of pull-back and push-forward functors on motivic constructible functions

Cely, Jorge; Raibaut, Michel

doi:10.48550/arxiv.1811.06850

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2018

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“…-This formula can be easily checked at the level of evaluation of points and can be proved at the level of the ring of constructible exponential functions by induction on the dimension, using cell decompositions and the construction of the motivic integral. A complete proof is given in [3].…”

Section: 8mentioning

confidence: 99%

Motivic wave front sets

Raibaut

2018

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The concept of wave front set was introduced in 1969-1970 by M. Sato in the hyperfunctions context ([1] and [34]) and by L. Hörmander ([23]) in the C ∞ context. Howe in [25] used the theory of wave front sets in the study of Lie groups representations. Heifetz in [22] 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 framework of [13] and [14] 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.

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Section: 8mentioning

confidence: 99%