Higher real K-theories and topological automorphic forms
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Behrens_K-theories.pdf
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Author(s)
Behrens, Mark Joseph
Hopkings, M. J.
Date Issued
January 2011
Journal
Journal of Topology
Publisher
Oxford University Press
Citation
Behrens, M., and M. J. Hopkins. “Higher real K-theories and topological automorphic forms.” Journal of Topology 4 (2011) 39–72. Copyright 2011 London Mathematical Society.
Version
Author's final manuscript
Abstract
Given a maximal finite subgroup G of the nth Morava stabilizer group at a prime p, we address the question: is the associated higher real K-theory EOn a summand of the K(n)-localization of a TAF -spectrum associated to a unitary similitude group of type U(1, n − 1)? We answer this question in the affirmative for p ∈ {2, 3, 5, 7} and n = (p − 1)p(superscript r−1) for a maximal finite subgroup containing an element of order p(superscript r). We answer the question in the negative for all other odd primary cases. In all odd primary cases, we give an explicit presentation of a global division algebra with involution in which the group G embeds unitarily.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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