Volume 13, issue 2 (2013)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The $\mathbb{G}_m$–equivariant motivic cohomology of Stiefel varieties

Ben Williams

Algebraic & Geometric Topology 13 (2013) 747–793
Abstract

We derive a version of the Rothenberg–Steenrod, fiber-to-base, spectral sequence for cohomology theories represented in model categories of simplicial presheaves. We then apply this spectral sequence to calculate the equivariant motivic cohomology of GLn with a general Gm–action; this coincides with the equivariant higher Chow groups. The motivic cohomology of PGLn and some of the equivariant motivic cohomology of a Stiefel variety, V m(An), with a general Gm–action is deduced as a corollary.

Keywords
Equivariant, Motivic cohomology, Chow group, Fiber-to-base, Stiefel, Projective general linear group
Mathematical Subject Classification 2010
Primary: 19E15
Secondary: 14C15, 18G55
References
Publication
Received: 28 March 2012
Revised: 2 August 2012
Accepted: 6 August 2012
Published: 24 March 2013
Authors
Ben Williams
Department of Mathematics
University of Southern California
Kaprielian Hall
3620 South Vermont Avenue
Los Angeles, CA 90089-2532
USA