| Description |
1 online resource (xxiii, 136 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; number 958 |
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Memoirs of the American Mathematical Society ; no. 958.
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| Contents |
Introduction -- p-divisible groups -- The Honda-Tate classification -- Tate modules and level structures -- Polarizations -- Forms and involutions -- Shimura varieties of type U (1, n-1) -- Deformation theory -- Topological automorphic forms -- Relationship to automorphic forms -- Smooth G-spectra -- Operation on TAF -- Buildings -- Hypercohomology of adele groups -- K(n)-local theory -- Example: chromatic level 1 |
| Summary |
"We apply a theorem of J. Lurie to produce cohomology theories associated to certain Shimura varieties of type U(1, n-1). These cohomology theories of topological automorphic forms (TAF) are related to Shimura varieties in the same way that TMF is related to the moduli space of elliptic curves. We study the cohomology operations on these theories, and relate them to certain Hecke algebras. We compute the K(n)-local homotopy types of these cohomology theories, and determine that K(n)-locally these spectra are given by finite products of homotopy fixed point spectra of the Morava E-theory E[subscript n] by finite subgroups of the Morava stabilizer group. We construct spectra Q[subscript U](K) for compact open subgroups K of certain adele groups, generalizing the spectra Q(ℓ) studied by the first author in the modular case. We show that the spectra Q[subscript U] (K) admit finite resolutions by the spectra TAF, arising from the theory of buildings. We prove that the K(n)-localizations of the spectra Q[subscript U] (K) are finite products of homotopy fixed point spectra of En with respect to certain arithmetic subgroups of the Morava stabilizer groups, which N. Naumann has shown (in certain cases) to be dense. Thus the spectra Q[subscript U] (K) approximate the K(n)-local sphere to the same degree that the spectra Q(ℓ) approximate the K(2)-local sphere."--Page v |
| Notes |
"Volume 204, number 958 (second of 5 numbers)." |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Automorphic forms.
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Algebraic topology.
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Homotopy groups.
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Shimura varieties.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Algebraic topology
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Automorphic forms
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Homotopy groups
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Shimura varieties
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Algebraische Topologie
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Automorphe Form
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Fundamentalgruppe
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| Form |
Electronic book
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| Author |
Lawson, Tyler, 1977-
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| ISBN |
9781470405724 |
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1470405725 |
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