On non-Archimedean and motivic distributions defined by kernels

TL;DR

This paper extends Schwartz kernel theorems to p-adic and motivic distributions, relating wave front sets of distributions and kernels using advanced integration techniques.

Contribution

It introduces a Schwartz kernel theorem for p-adic and motivic distributions and explores the relationship between wave front sets in these contexts.

Findings

Established a Schwartz kernel theorem for p-adic distributions.

Extended the theorem to motivic distributions using motivic integration.

Provided relations between wave front sets of distributions and their kernels.

Abstract

As in real microlocal analysis, we prove a Schwartz kernel theorem for $p$-adic distributions. We extend this result for motivic distributions using Cluckers-Loeser's motivic integration. In both settings, we give also a relation between the wave front sets of the distribution and its kernel.