On the torsion of Chow groups of Severi-Brauer varieties

TL;DR

This paper extends Karpenko's results on torsion in Chow groups of Severi-Brauer varieties to higher degrees, revealing new torsion phenomena, bounds, and algebra indecomposability insights.

Contribution

It generalizes torsion results to higher gamma filtration degrees, providing new bounds and applications to algebra indecomposability.

Findings

Identified nontrivial torsion in higher Chow groups

Established upper bounds for torsion subgroup annihilators

Proved indecomposability of certain algebras

Abstract

In this paper, we generalize a result of Karpenko on the torsion in the second quotient of the gamma filtration for Severi-Brauer varieties to higher degrees. As an application, we provide a nontrivial torsion in higher Chow groups and the topological filtration of the associated generic variety and obtain new upper bounds for the annihilators of the torsion subgroups in the Chow groups of a large class of Severi-Brauer varieties. In particular, using the torsion in higher degrees, we show indecomposability of certain algebras.