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arXiv · 2608.22501

A motivic derived Fourier transform

Tong Zhou
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Abstract

We construct a theory of Fourier transform for rational \'etale motives on derived vector bundles over derived Artin stacks over a field of positive characteristic, defined as the integral transform with kernel the Artin-Schreier motive. The basic properties are established: involutivity, base change, functoriality, duality, monodromicity, constructibility, and compatibilities with various natural transformations.

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Tong Zhou. 2026-08-23. A motivic derived Fourier transform. https://arxiv.org/abs/2608.22501

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