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arXiv · 2511.00001

Incarnations of the Fourier Transform in Algebraic Geometry

Paul Immanuel
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Abstract

An exploration into the uses of the Fourier transform in the areas of algebraic and arithmetic geometry. In particular this treats the topics of Banach-Colmez spaces, for which an introduction to the theory of perfectoid spaces is given. The ideas closely follow work by Dr. Johannes Ansch\"utz and Arthur-C\'esar Le Bras in their 2021 paper entitled 'A Fourier Transform for Banach-Colmez spaces'. This thesis builds up the motivation for this work by starting with the l-adic Fourier transform, and a related transform in the case of perfect unipotent group schemes.

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Paul Immanuel. 2025-09-14. Incarnations of the Fourier Transform in Algebraic Geometry. https://arxiv.org/abs/2511.00001

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