The Morava E-theories of finite general linear groups

2010/01/12 by S. Marsh, Sam Marsh, Marsh, Sam · 2 citations
Mathematics · #55N20 #55N22 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:55N20 #msc:55N22

paper · pdf · doi:10.48550/arxiv.1001.1949

PhD Thesis, University of Sheffield, 2009, Supervisor: Neil Strickland (95 pages)

arxiv created 2010/01/12 · openalex publication_date 2010/01/12 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By studying the representation theory of a certain infinite p-group and using the generalised characters of Hopkins, Kuhn and Ravenel we find useful ways of understanding the rational Morava E-theory of the classifying spaces of general linear groups over finite fields. Making use of the well understood theory of formal group laws we establish more subtle results integrally, building on relevant work of Tanabe. In particular, we study in detail the cases where the group has dimension less than or equal to the prime p at which the E-theory is localised.

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