Higher real K-theories and topological automorphic forms
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 af...
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| Format: | Article |
| Language: | en_US |
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Oxford University Press
2011
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| Online Access: | http://hdl.handle.net/1721.1/61381 |
| _version_ | 1811084674801336320 |
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| author | Behrens, Mark Joseph Hopkings, M. J. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Behrens, Mark Joseph Hopkings, M. J. |
| author_sort | Behrens, Mark Joseph |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T12:55:16Z |
| format | Article |
| id | mit-1721.1/61381 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:55:16Z |
| publishDate | 2011 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | mit-1721.1/613812022-10-01T11:53:49Z Higher real K-theories and topological automorphic forms Behrens, Mark Joseph Hopkings, M. J. Massachusetts Institute of Technology. Department of Mathematics Behrens, Mark Joseph Behrens, Mark Joseph 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. National Science Foundation (U.S.) Alfred P. Sloan Foundation United States. Defense Advanced Research Projects Agency (DARPA) 2011-03-03T14:24:30Z 2011-03-03T14:24:30Z 2011-01 2009-10 Article http://purl.org/eprint/type/JournalArticle 1753-8424 1753-8416 http://hdl.handle.net/1721.1/61381 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. en_US Journal of Topology Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Oxford University Press MIT web domain |
| spellingShingle | Behrens, Mark Joseph Hopkings, M. J. Higher real K-theories and topological automorphic forms |
| title | Higher real K-theories and topological automorphic forms |
| title_full | Higher real K-theories and topological automorphic forms |
| title_fullStr | Higher real K-theories and topological automorphic forms |
| title_full_unstemmed | Higher real K-theories and topological automorphic forms |
| title_short | Higher real K-theories and topological automorphic forms |
| title_sort | higher real k theories and topological automorphic forms |
| url | http://hdl.handle.net/1721.1/61381 |
| work_keys_str_mv | AT behrensmarkjoseph higherrealktheoriesandtopologicalautomorphicforms AT hopkingsmj higherrealktheoriesandtopologicalautomorphicforms |