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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

We study the Morava E–theory (at a prime p) of BGL d(F), where F is a finite field with |F| = 1(modp). Taking all d together, we obtain a structure with two products × and . We prove that it is a polynomial ring under × and that the module of ×–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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Morava K–theory, general linear groups
Mathematical Subject Classification 2010
Primary: 55N20
Secondary: 14L05, 55N22, 55R35
Received: 17 October 2019
Revised: 16 February 2021
Accepted: 10 April 2021
Published: 10 October 2022
Samuel M A Hutchinson
United Kingdom
Samuel J Marsh
School of Mathematics and Statistics
The University of Sheffield
United Kingdom
Neil P Strickland
School of Mathematics and Statistics
The University of Sheffield
United Kingdom