The 𝔾m–equivariant motivic cohomology of Stiefel varieties

Williams, Ben

doi:10.2140/agt.2013.13.747

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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The $\mathbb{G}_m$–equivariant motivic cohomology of Stiefel varieties

Ben Williams

Algebraic & Geometric Topology 13 (2013) 747–793

DOI: 10.2140/agt.2013.13.747

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 ${GL}_{n}$ with a general $G_{m}$ –action; this coincides with the equivariant higher Chow groups. The motivic cohomology of ${PGL}_{n}$ and some of the equivariant motivic cohomology of a Stiefel variety, $V_{m} (A^{n})$ , with a general $G_{m}$ –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

Volume 13, issue 2 (2013)