Lannes’s T–functor and equivariant Chow rings

Hemminger, David

doi:10.2140/agt.2021.21.1881

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

David Hemminger

Algebraic & Geometric Topology 21 (2021) 1881–1910

DOI: 10.2140/agt.2021.21.1881

Abstract

For $X$ a smooth scheme acted on by a linear algebraic group $G$ and $p$ a prime, the equivariant Chow ring ${CH}_{G}^{*} (X) \otimes 𝔽_{p}$ is an unstable algebra over the Steenrod algebra. We compute Lannes’s $T$ –functor applied to ${CH}_{G}^{*} (X) \otimes 𝔽_{p}$ . As an application, we compute the localization of ${CH}_{G}^{*} (X) \otimes 𝔽_{p}$ 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

Volume 21, issue 4 (2021)