2025/09/14 by Paul Immanuel, Immanuel, Paul
Mathematics · #advanced mathematical theories #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.2511.00001
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 Anschütz and Arthur-César 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.