A Fourier Transform for Banach-Colmez spaces

2021/11/22 by Johannes Anschütz, Anschütz, Johannes, Arthur-César Le Bras +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · doi:10.48550/arxiv.2111.11116

openalex publication_date 2021/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define and study an ℓ-adic Fourier transform for a relative version of Banach-Colmez spaces (over a perfectoid space which is not necessarily a geometric point), which can be thought of as some analytic analogue of the ℓ-adic Fourier transform for unipotent perfect group schemes. We explicitly describe it on some examples.

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