A Fourier Transform for Banach-Colmez spaces

Johannes Anschütz , Arthur-César Le Bras (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

We define and study an $\ell$-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 $\ell$-adic Fourier transform for unipotent perfect group schemes. We explicitly describe it on some examples.

Domaines: Mathématiques [math]

Johannes Anschütz, Arthur-César Le Bras. A Fourier Transform for Banach-Colmez spaces. 2021. ⟨hal-03444442⟩