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Topological Automorphic Forms
 
Mark Behrens Massachusetts Institute of Technology, Cambridge, MA
Tyler Lawson University of Minnesota, Minneapolis, MN
Topological Automorphic Forms
eBook ISBN:  978-1-4704-0572-4
Product Code:  MEMO/204/958.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
Topological Automorphic Forms
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Topological Automorphic Forms
Mark Behrens Massachusetts Institute of Technology, Cambridge, MA
Tyler Lawson University of Minnesota, Minneapolis, MN
eBook ISBN:  978-1-4704-0572-4
Product Code:  MEMO/204/958.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2042009; 136 pp
    MSC: Primary 55; Secondary 11;

    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
     
     
    • Chapters
    • Introduction
    • 1. $p$-divisible groups
    • 2. The Honda-Tate classification
    • 3. Tate modules and level structures
    • 4. Polarizations
    • 5. Forms and involutions
    • 6. Shimura varieties of type $U(1,n-1)$
    • 7. Deformation theory
    • 8. Topological automorphic forms
    • 9. Relationship to automorphic forms
    • 10. Smooth $G$-spectra
    • 11. Operations on $\mathit {TAF}$
    • 12. Buildings
    • 13. Hypercohomology of adele groups
    • 14. $K(n)$-local theory
    • 15. Example: chromatic level $1$
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2042009; 136 pp
MSC: Primary 55; Secondary 11;

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.

  • Chapters
  • Introduction
  • 1. $p$-divisible groups
  • 2. The Honda-Tate classification
  • 3. Tate modules and level structures
  • 4. Polarizations
  • 5. Forms and involutions
  • 6. Shimura varieties of type $U(1,n-1)$
  • 7. Deformation theory
  • 8. Topological automorphic forms
  • 9. Relationship to automorphic forms
  • 10. Smooth $G$-spectra
  • 11. Operations on $\mathit {TAF}$
  • 12. Buildings
  • 13. Hypercohomology of adele groups
  • 14. $K(n)$-local theory
  • 15. Example: chromatic level $1$
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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