Topological automorphic forms

General Introduction

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The original article by Behrens and Lawson

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Paper References

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Definition

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Properties

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Standard theorems

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Open Problems

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Connections to Number Theory

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Computations and Examples

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History and Applications

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Some Research Articles

arXiv:0910.0617 Higher real K-theories and topological automorphic forms from arXiv Front: math.AT by Mark Behrens, Michael J. Hopkins 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 EO_n 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 in {2, 3, 5, 7} and n = (p-1)p^{r-1} for a maximal finite subgroup containing an element of order p^r. We answer the question in the negative for all other odd primary cases. In all odd primary cases, we to give an explicit presentation of a global division algebra with involution in which the group G embeds unitarily.

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General Introduction