Progress in Mathematics

Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change

Authors: Getz, Jayce, Goresky, Mark

  • Award winning monograph of the 2011 Ferran Sunyer i Balaguer Prize competition
  • Contains basic material on intersection cohomology, modular cycles and automorphic forms from the classical and adèlic points of view
  •  Appendices on orbifolds, Fourier expansions, and base change help to make the book self-contained
  • Contains topics of interest for geometers and number theorists interested in locally symmetric spaces and automorphic forms
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  • ISBN 978-3-0348-0351-9
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Hardcover $139.00
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  • ISBN 978-3-0348-0350-2
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  • ISBN 978-3-0348-0795-1
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About this book

In the 1970s Hirzebruch and Zagier produced elliptic modular forms with coefficients in the homology of a Hilbert modular surface. They then computed the Fourier coefficients of these forms in terms of period integrals and L-functions. In this book the authors take an alternate approach to these theorems and generalize them to the setting of Hilbert modular varieties of arbitrary dimension. The approach is conceptual and uses tools that were not available to Hirzebruch and Zagier, including intersection homology theory, properties of modular cycles, and base change. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular forms are presented both in the classical and adèlic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces.

Table of contents (11 chapters)

  • Introduction

    Getz, Jayce (et al.)

    Pages 1-19

  • Review of Chains and Cochains

    Getz, Jayce (et al.)

    Pages 21-28

  • Review of Intersection Homology and Cohomology

    Getz, Jayce (et al.)

    Pages 29-39

  • Review of Arithmetic Quotients

    Getz, Jayce (et al.)

    Pages 41-55

  • Generalities on Hilbert Modular Forms and Varieties

    Getz, Jayce (et al.)

    Pages 57-89

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-0348-0351-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-3-0348-0350-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-3-0348-0795-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change
Authors
Series Title
Progress in Mathematics
Series Volume
298
Copyright
2012
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0351-9
DOI
10.1007/978-3-0348-0351-9
Hardcover ISBN
978-3-0348-0350-2
Softcover ISBN
978-3-0348-0795-1
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XIV, 258
Topics