ENGLISH

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

By Jayce Getz , Mark Goresky (auth.)

Book information

Publisher
Birkhäuser Basel
Year
2012
ISBN
3034803508, 9783034803502
DOI
10.1007/978-3-0348-0351-9
Language
english
Format
PDF
Filesize
12 MB (12760136 bytes)
Series
Progress in Mathematics 298
Volume
298
Edition
1
Pages
258\263
Orientation
no
Scanned
no
Time added
2012-04-10 14:27:24
Number Theory; Algebraic Geometry

Description

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.

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