Another look at $p$-adic Fourier-theory

TL;DR

This paper connects $p$-adic Fourier theory to the classification of $p$-divisible groups, providing a straightforward generalization based on Scholze and Weinstein's work, though it has been superseded by a more comprehensive follow-up.

Contribution

It shows that a natural generalization of $p$-adic Fourier theory follows from existing classification results, simplifying the understanding of the theory.

Findings

The generalization follows immediately from Scholze and Weinstein's classification.

The paper's results are extended and generalized in a subsequent work.

It provides a conceptual link between Fourier theory and $p$-divisible groups.

Abstract

In this short note, we show that a natural generalization of the $p$-adic Fourier theory of Schneider and Teitelbaum follows immediately from the classification of $p$-divisible groups over $\cal{O}_{\mathbb{C}_p}$ by Scholze and Weinstein. This paper has been superseded by [arXiv:2603.15446], where the results are extended and generalized.