Truncated Barsotti-Tate Groups and Displays

TL;DR

This paper introduces a new framework for understanding truncated Barsotti-Tate groups using truncated displays, establishing connections with crystals and functors over rings where p is nilpotent.

Contribution

It defines truncated displays over rings with nilpotent p, associates crystals to them, and constructs functors to truncated Barsotti-Tate groups, advancing the theory in this area.

Findings

Established a correspondence between truncated displays and crystals.

Constructed functors from truncated displays to Barsotti-Tate groups.

Extended the theory to rings with nilpotent prime p.

Abstract

We define truncated displays over rings in which a prime p is nilpotent, we associate crystals to truncated displays, and we define functors from truncated displays to truncated Barsotti-Tate groups.