Invariant functions on p-divisible groups and the p-adic Corona problem

TL;DR

This paper investigates invariant functions on reductions of p-divisible groups, combining Tate's results with van der Put's solution to address the p-adic Corona problem, with extensions needed for higher dimensions.

Contribution

It extends the understanding of invariant functions on p-divisible groups by linking Tate's work with the p-adic Corona problem, providing new insights for one-dimensional cases.

Findings

Main result applies to one-dimensional p-divisible groups

Combines Tate's results with van der Put's solution

Highlights the need for a generalized p-adic Corona problem for higher dimensions

Abstract

We study invariant functions on the reductions mod p^n of p-divisible groups. The proof of the main result, which applies to one-dimensional groups, combines results of Tate with van der Put's solution of his p-adic Corona problem. For higher dimensional groups a generalization of the p-adic Corona problem would have to be solved.