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On non-Archimedean and motivic distributions defined by kernels

Téofil Adamski

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.

On non-Archimedean and motivic distributions defined by kernels

Abstract

As in real microlocal analysis, we prove a Schwartz kernel theorem for -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.

Paper Structure

This paper contains 15 sections, 215 equations.

Table of Contents

  1. Kernels of p-adic distributions
  2. Distributions and Schwartz kernel theorem
  3. Wave front sets and kernels
  4. Kernels of motivic distributions
  5. Motivic integration
  6. A brief overview
  7. Convolution product
  8. Schwartz--Bruhat functions
  9. Tensor product on Schwartz--Bruhat functions
  10. Definable distributions
  11. Motivic Schwartz kernel theorem
  12. Wave front sets of kernels
  13. Induced distributions
  14. Microlocally smooth definable data and kernels
  15. Wave front sets and kernels

Theorems & Definitions (13)

  • proof
  • proof
  • proof
  • proof : Proof of Theorem \ref{['thm:kernel-p']}
  • proof
  • proof
  • proof
  • proof
  • proof : Proof of Theorem \ref{['thm:kernel-mot']}
  • proof
  • ...and 3 more