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Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change
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 the...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Basel :
Springer Basel : Imprint: Birkhäuser,
2012.
|
| Edición: | 1st ed. 2012. |
| Colección: | Progress in Mathematics,
298 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-3-0348-0351-9 | ||
| 003 | DE-He213 | ||
| 005 | 20220114130009.0 | ||
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| 008 | 120328s2012 sz | s |||| 0|eng d | ||
| 020 | |a 9783034803519 |9 978-3-0348-0351-9 | ||
| 024 | 7 | |a 10.1007/978-3-0348-0351-9 |2 doi | |
| 050 | 4 | |a QA241-247.5 | |
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| 082 | 0 | 4 | |a 512.7 |2 23 |
| 100 | 1 | |a Getz, Jayce. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change |h [electronic resource] / |c by Jayce Getz, Mark Goresky. |
| 250 | |a 1st ed. 2012. | ||
| 264 | 1 | |a Basel : |b Springer Basel : |b Imprint: Birkhäuser, |c 2012. | |
| 300 | |a XIV, 258 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Progress in Mathematics, |x 2296-505X ; |v 298 | |
| 505 | 0 | |a 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 adèlic facts -- Appendix D. Fourier expansions of Hilbert modular forms -- Appendix E. Review of Prime Degree Base Change for GL2 -- Bibliography. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Number theory. | |
| 650 | 0 | |a Algebraic geometry. | |
| 650 | 1 | 4 | |a Number Theory. |
| 650 | 2 | 4 | |a Algebraic Geometry. |
| 700 | 1 | |a Goresky, Mark. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783034807951 |
| 776 | 0 | 8 | |i Printed edition: |z 9783034803526 |
| 776 | 0 | 8 | |i Printed edition: |z 9783034803502 |
| 830 | 0 | |a Progress in Mathematics, |x 2296-505X ; |v 298 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-0348-0351-9 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||