Hilbert modular forms with coefficients in intersection homology and quadratic base change
 Author/Creator
 Getz, Jayce.
 Language
 English.
 Imprint
 Basel ; New York : Birkhäuser, c2012.
 Physical description
 xiii, 256 p. : ill ; 24 cm.
 Series
 Progress in mathematics (Boston, Mass.) v. 298.
Access
Contributors
 Contributor
 Goresky, Mark, 1950
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 237247) and indexes.
 Contents

 Chapter 1. Introduction. Chapter 2. Review of Chains and Cochains. Chapter 3. Review of Intersection Homology and Cohomology. Chapter 4. Review of Arithmetic Quotients. Chapter 5. Generalities on Hilbert Modular Forms and Varieties. Chapter 6. Automorphic vector bundles and local systems. Chapter 7. The automorphic description of intersection cohomology. Chapter 8. Hilbert Modular Forms with Coefficients in a Hecke Module. Chapter 9. Explicit construction of cycles. Chapter 10. The full version of Theorem 1.3. Chapter 11. Eisenstein Series with Coefficients in Intersection Homology. Appendix A. Proof of Proposition 2.4. Appendix B. Recollections on Orbifolds. Appendix C. Basic adelic facts. Appendix D. Fourier expansions of Hilbert modular forms. Appendix E. Review of Prime Degree Base Change for GL2. Bibliography.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 Lfunctions. 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 adelic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2012
 Responsibility
 Jayce Getz, Mark Goresky.
 Series
 Progress in mathematics ; v. 298
 ISBN
 9783034803502 (alk. paper)
 3034803508 (alk. paper)
 9783034803519 (ebk.)
 3034803516 (ebk.)