A Microlocal Theory for Zariski-Constructible Sheaves on Rigid Analytic Varieties

TL;DR

This paper develops a microlocal framework for Zariski-constructible sheaves on rigid analytic varieties, extending microlocal analysis tools to non-Archimedean geometry.

Contribution

It introduces a microlocal theory for these sheaves, including definitions and properties of monodromic sheaves, Fourier transform, and singular support in the rigid analytic setting.

Findings

Established a microlocal theory for Zariski-constructible sheaves

Defined monodromic sheaves and Fourier transform in this context

Formulated conjectures and provided categorical characterisations

Abstract

We develop a microlocal theory, in the sense of Kashiwara-Schapira, for Zariski-constructible sheaves on rigid analytic varieties. We define and study monodromic sheaves, the monodromic Fourier transform, specialisation, microlocalisation, micro-hom, and singular support in this context. Some questions and conjectures are formulated in the end. The appendix contains infinity-categorical characterisations of monodromic sheaves.