000			03228nam a22004695i 4500
001			978-3-0348-0351-9
003			DE-He213
005			20140220083253.0
007			cr nn 008mamaa
008			120328s2012 sz | s |||| 0|eng d
020			_a9783034803519 _9978-3-0348-0351-9
024	7		_a10.1007/978-3-0348-0351-9 _2doi
050		4	_aQA241-247.5
072		7	_aPBH _2bicssc
072		7	_aMAT022000 _2bisacsh
082	0	4	_a512.7 _223
100	1		_aGetz, Jayce. _eauthor.
245	1	0	_aHilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change _h[electronic resource] / _cby Jayce Getz, Mark Goresky.
264		1	_aBasel : _bSpringer Basel, _c2012.
300			_aXIII, 256p. 5 illus., 1 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aProgress in Mathematics ; _v298
505	0		_aChapter 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 adèlic facts -- Appendix D. Fourier expansions of Hilbert modular forms -- Appendix E. Review of Prime Degree Base Change for GL2 -- Bibliography.
520			_aIn 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.
650		0	_aMathematics.
650		0	_aGeometry, algebraic.
650		0	_aNumber theory.
650	1	4	_aMathematics.
650	2	4	_aNumber Theory.
650	2	4	_aAlgebraic Geometry.
700	1		_aGoresky, Mark. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783034803502
830		0	_aProgress in Mathematics ; _v298
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-0348-0351-9
912			_aZDB-2-SMA
999			_c101730 _d101730