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arXiv · 2507.18604

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

Tong Zhou
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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.

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Tong Zhou. 2025-07-24. A Microlocal Theory for Zariski-Constructible Sheaves on Rigid Analytic Varieties. https://arxiv.org/abs/2507.18604

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