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Author Getz, Jayce.
Title Hilbert modular forms with coefficients in intersection homology and quadratic base change / Jayce Getz, Mark Goresky.
Imprint Basel : Birkhauser, 2012.

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Author Getz, Jayce.
Series Progress in mathematics ; v. 298
Progress in mathematics (Boston, Mass.) ; v. 298.
Subject Hilbert modular surfaces.
Intersection homology theory.
Alt Name Goresky, Mark, 1950-
Description 1 online resource (xiii, 256 pages).
polychrome rdacc
Bibliography Note Includes bibliographical references and indexes.
Contents Introduction / Review of Chains and Cochains / Review of Intersection Homology and Cohomology / Review of Arithmetic Quotients / Generalities on Hilbert Modular Forms and Varieties / Automorphic Vector Bundles and Local Systems / The Automorphic Description of Intersection Cohomology / Hilbert Modular Forms with Coefficients in a Hecke Module / Explicit Construction of Cycles / The Full Version of Theorem 1.3 / Eisenstein Series with Coefficients in Intersection Homology.
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 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 adelic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces.
ISBN 9783034803519 (electronic bk.)
3034803516 (electronic bk.)
OCLC # 785149448
Additional Format Print version: Getz, Jayce. Hilbert modular forms with coefficients in intersection homology and quadratic base change. Basel : Birkhauser, 2012 (DLC) 2012936073

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