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© 2012

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

Benefits

  • 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

Book

Part of the Progress in Mathematics book series (PM, volume 298)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Jayce Getz, Mark Goresky
    Pages 1-19
  3. Jayce Getz, Mark Goresky
    Pages 21-28
  4. Jayce Getz, Mark Goresky
    Pages 29-39
  5. Jayce Getz, Mark Goresky
    Pages 41-55
  6. Jayce Getz, Mark Goresky
    Pages 57-89
  7. Jayce Getz, Mark Goresky
    Pages 91-110
  8. Jayce Getz, Mark Goresky
    Pages 111-134
  9. Jayce Getz, Mark Goresky
    Pages 135-150
  10. Jayce Getz, Mark Goresky
    Pages 151-166
  11. Jayce Getz, Mark Goresky
    Pages 167-177
  12. Jayce Getz, Mark Goresky
    Pages 179-182
  13. Back Matter
    Pages 183-256

About this book

Introduction

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.

Keywords

Fourier coefficients Hecke operators Hilbert modular varieties automorphic forms intersection cohomology

Authors and affiliations

  1. 1., Department of MathematicsMcGill UniversityMontrealCanada
  2. 2., School of MathematicsInstitute for Advanced StudyPrincetonUSA

Bibliographic information

  • Book Title Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change
  • Authors Jayce Getz
    Mark Goresky
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI https://doi.org/10.1007/978-3-0348-0351-9
  • Copyright Information Springer Basel 2012
  • Publisher Name Springer, Basel
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-0348-0350-2
  • Softcover ISBN 978-3-0348-0795-1
  • eBook ISBN 978-3-0348-0351-9
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages XIV, 258
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Number Theory
    Algebraic Geometry
  • Buy this book on publisher's site
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