# Schubert cycles and subvarieties of generalized Severi-Brauer varieties

## TL;DR

This paper investigates the structure of twisted Schubert cells in generalized Severi-Brauer varieties, demonstrating torsion-free properties of certain Chow groups through K-theory techniques.

## Contribution

It introduces new results on the torsion properties of codimension 2 Chow groups of these varieties, expanding understanding of their algebraic and geometric structure.

## Key findings

- Codimension 2 Chow groups are torsion free in specific cases.
- Utilizes topological filtration on K-theory to analyze Chow groups.
- Provides new insights into the structure of twisted Schubert cells.

## Abstract

We study twisted forms of Schubert cells in generalized Severi-Brauer varieties, and show that the codimension $2$ Chow groups of these varieties are torsion free in certain cases, using the topological filtration on their K-theory