The Morava E-theories of finite general linear groups

Details The Morava E-theories of finite general linear groups The Morava E-theories of finite general linear groups

2010-01-12

arxiv.org/abs/1001.1949v1

Mathematics

Algebraic Topology

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

Scientific paper

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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