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Lannes's $T$–functor and equivariant Chow rings

David Hemminger

Algebraic & Geometric Topology 21 (2021) 1881–1910
Abstract

For X a smooth scheme acted on by a linear algebraic group G and p a prime, the equivariant Chow ring CHG(X) 𝔽p is an unstable algebra over the Steenrod algebra. We compute Lannes’s T–functor applied to CHG(X) 𝔽p. As an application, we compute the localization of CHG(X) 𝔽p away from n–nilpotent modules over the Steenrod algebra, affirming a conjecture of Totaro as a special case. The case when X is a point and n = 1 generalizes and recovers an algebrogeometric version of Quillen’s stratification theorem proved by Yagita and Totaro.

Keywords
Chow ring, equivariant Chow ring, group cohomology, Steenrod algebra, unstable modules, unstable algebras, $T$–functor
Mathematical Subject Classification 2010
Primary: 14C15, 55S10
Secondary: 14L30, 55N91
References
Publication
Received: 16 December 2019
Revised: 23 June 2020
Accepted: 24 August 2020
Published: 18 August 2021
Authors
David Hemminger
Department of Mathematics
University of California, Los Angeles
Los Angeles, CA
United States