Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change
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Beschreibung
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.
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.
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 Includes supplementary material: sn.pub/extras
Autor*in
Jayce Getz
Themen in »Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change«
Fourier coefficients Hecke operators Hilbert modular varieties automorphic forms intersection cohomology