The Motivic Cohomology of Stiefel Varieties

TL;DR

This paper computes the motivic cohomology of Stiefel varieties, detailing their ring structure and power operations, using a comparison with linear groups and projective spaces.

Contribution

It provides the first detailed computation of motivic cohomology for Stiefel varieties, including ring structure and operations, advancing understanding in algebraic geometry.

Findings

Computed motivic cohomology of Stiefel varieties

Described ring structure and power operations

Linked linear groups with projective spaces

Abstract

The main result of this paper is a computation of the motivic cohomology of varieties of n \times m-matrices of of rank m, including both the ring structure and the action of the reduced power operations. The argument proceeds by a comparison of the general linear group-scheme with a Tate suspension of a space which is A1-equivalent to projective n - 1-space with a disjoint basepoint.