Incarnations of the Fourier Transform in Algebraic Geometry
Algebraic Geometry
2025-11-04 v1
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.
Keywords
Cite
@article{arxiv.2511.00001,
title = {Incarnations of the Fourier Transform in Algebraic Geometry},
author = {Paul Immanuel},
journal= {arXiv preprint arXiv:2511.00001},
year = {2025}
}