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A motivic derived Fourier transform
Tong Zhou
We construct a theory of Fourier transform for rational étale motives on derived vector bundles over derived Artin stacks over a field of positive characteristic, defined as the in…
A Microlocal Theory for Zariski-Constructible Sheaves on Rigid Analytic Varieties
Tong Zhou
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 monod…
Vanishing Cycles for Zariski-Constructible Sheaves on Rigid Analytic Varieties
Tong Zhou
We develop a theory of nearby and vanishing cycles in the context of finite-coefficient Zariski-constructible sheaves over a non-archimedean field which is non-trivially valued, co…
The Fourier Transform and Characteristic Cycles of Monodromic -adic Sheaves
Tong Zhou
Brylinski and Malgrange proved in 1986 that, for a monodromic algebraic D-module on a finite dimensional vector space over the complex numbers, its characteristic cycle is canonica…