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The Morava E-theories of finite general linear groups

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arxiv 1001.1949 v1 pith:NNZNWNM4 submitted 2010-01-12 math.AT

Sam Marsh This is my paper · ORCID
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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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Cited by 1 Pith paper

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  1. The Lubin-Tate Theory of Configuration Spaces: I

    math.AT 2019-08 accept novelty 8.0 of 10

    A new Hecke spectral sequence computes the Morava E-theory of unordered configuration spaces, yielding explicit E-theory and F_p-homology results for p-point configurations.

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