On a theorem of Scholze-Weinstein

TL;DR

This paper provides a self-contained proof of a theorem by Scholze-Weinstein that characterizes the Tate module of p-divisible groups over perfect fields using Dieudonne modules, clarifying its relation to classical descriptions.

Contribution

It offers a complete proof of the Scholze-Weinstein theorem and elucidates its connection with classical Dieudonne theory.

Findings

The Tate module G can be reconstructed from the Dieudonne module of H.

The theorem applies to good semiperfect k-algebras C.

The proof clarifies the relation between modern and classical descriptions of p-divisible groups.

Abstract

Let G be the Tate module of a p-divisble group H over a perfect field k of characteristic p. A theorem of Scholze-Weinstein describes G (and therefore H itself) in terms of the Dieudonne module of H; more precisely, it describes G(C) for "good" semiperfect k-algebras C (which is enough to reconstruct G). In these notes we give a self-contained proof of this theorem and explain the relation with the classical descriptions of the Dieudonne functor from Dieudonne modules to p-divisible groups.