Chromatic (co)homology of finite general linear groups

Hutchinson, Samuel M A; Marsh, Samuel J; Strickland, Neil P

doi:10.2140/agt.2022.22.1511

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Chromatic (co)homology of finite general linear groups

Samuel M A Hutchinson, Samuel J Marsh and Neil P Strickland

Algebraic & Geometric Topology 22 (2022) 1511–1614

DOI: 10.2140/agt.2022.22.1511

Abstract

We study the Morava $E$ –theory (at a prime $p$ ) of $B {GL}_{d} (F)$ , where $F$ is a finite field with $| F | = 1 (\mod p)$ . Taking all $d$ together, we obtain a structure with two products $\times$ and $∙$ . We prove that it is a polynomial ring under $\times$ and that the module of $\times$ –indecomposables inherits a $∙$ –product, and we describe the structure of the resulting ring. In the process, we prove many auxiliary structural results.

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Keywords

Morava K–theory, general linear groups

Mathematical Subject Classification 2010

Primary: 55N20

Secondary: 14L05, 55N22, 55R35

References

Publication

Received: 17 October 2019

Revised: 16 February 2021

Accepted: 10 April 2021

Published: 10 October 2022

Authors

Samuel M A Hutchinson
Macclesfield United Kingdom
https://sites.google.com/site/samhutchinsonresearch/
Samuel J Marsh
School of Mathematics and Statistics The University of Sheffield Sheffield United Kingdom
https://sam-marsh.staff.shef.ac.uk/
Neil P Strickland
School of Mathematics and Statistics The University of Sheffield Sheffield United Kingdom
https://neil-strickland.staff.shef.ac.uk/

Volume 22, issue 4 (2022)