On the Chow Ring of the Stack of truncated Barsotti-Tate Groups

TL;DR

This paper computes the Chow ring of the stack of truncated Barsotti-Tate groups and related structures, providing new algebraic insights into their geometric properties over fields of characteristic p.

Contribution

It determines the Chow ring of the stack of truncated displays and G-zips, and analyzes the pull-back morphism of the truncated display functor, advancing understanding of these algebraic stacks.

Findings

Chow ring of the stack of truncated displays explicitly computed

Chow ring of G-zips stack characterized

Chow ring of truncated Barsotti-Tate groups determined up to p-torsion

Abstract

We determine the Chow ring of the stack of truncated displays and more generally the Chow ring of the stack of G-zips. We also investigate the pull-back morphism of the truncated display functor. From this we can determine the Chow ring of the stack of truncated Barsotti-Tate groups over a field of characteristic p up to p-torsion.