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Topological Automorphic Forms
Mark Behrens, Massachusetts Institute of Technology, Cambridge, MA, and Tyler Lawson, University of Minnesota, Minneapolis, MN

Memoirs of the American Mathematical Society
2009; 136 pp; softcover
Volume: 204
ISBN-10: 0-8218-4539-X
ISBN-13: 978-0-8218-4539-4
List Price: US$78
Individual Members: US$46.80
Institutional Members: US$62.40
Order Code: MEMO/204/958
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The authors 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 (\(\mathit{TAF}\)) are related to Shimura varieties in the same way that \(\mathit{TMF}\) is related to the moduli space of elliptic curves.

Table of Contents

  • \(p\)-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 \(\mathit{TAF}\)
  • Buildings
  • Hypercohomology of adele groups
  • \(K(n)\)-local theory
  • Example: chromatic level \(1\)
  • Bibliography
  • Index
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