p-Adic Automorphic Forms on Shimura Varieties:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2004
|
| Schriftenreihe: | Springer Monographs in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme theoretic algebraic geometry: 1. An elementary construction of Shimura varieties as moduli of abelian schemes. 2. p-adic deformation theory of automorphic forms on Shimura varieties. 3. A simple proof of irreducibility of the generalized Igusa tower over the Shimura variety. The book starts with a detailed study of elliptic and Hilbert modular forms and reaches to the forefront of research of Shimura varieties associated with general classical groups. The method of constructing p-adic analytic families and the proof of irreducibility was recently discovered by the author. The area covered in this book is now a focal point of research worldwide with many far-reaching applications that have led to solutions of longstanding problems and conjectures. Specifically, the use of p-adic elliptic and Hilbert modular forms have proven essential in recent breakthroughs in number theory (for example, the proof of Fermat's Last Theorem and the Shimura-Taniyama conjecture by A. Wiles and others). Haruzo Hida is Professor of Mathematics at University of California, Los Angeles. His previous books include Modular Forms and Galois Cohomology (Cambridge University Press 2000) and Geometric Modular Forms and Elliptic Curves (World Scientific Publishing Company 2000) |
| Beschreibung: | 1 Online-Ressource (XI, 390 p) |
| ISBN: | 9781468493900 9781441919236 |
| ISSN: | 1439-7382 |
| DOI: | 10.1007/978-1-4684-9390-0 |
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-9390-0 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468493900 9781441919236 |
| issn | 1439-7382 |
| language | English |
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| spelling | Hida, Haruzo Verfasser aut p-Adic Automorphic Forms on Shimura Varieties by Haruzo Hida New York, NY Springer New York 2004 1 Online-Ressource (XI, 390 p) txt rdacontent c rdamedia cr rdacarrier Springer Monographs in Mathematics 1439-7382 This book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme theoretic algebraic geometry: 1. An elementary construction of Shimura varieties as moduli of abelian schemes. 2. p-adic deformation theory of automorphic forms on Shimura varieties. 3. A simple proof of irreducibility of the generalized Igusa tower over the Shimura variety. The book starts with a detailed study of elliptic and Hilbert modular forms and reaches to the forefront of research of Shimura varieties associated with general classical groups. The method of constructing p-adic analytic families and the proof of irreducibility was recently discovered by the author. The area covered in this book is now a focal point of research worldwide with many far-reaching applications that have led to solutions of longstanding problems and conjectures. Specifically, the use of p-adic elliptic and Hilbert modular forms have proven essential in recent breakthroughs in number theory (for example, the proof of Fermat's Last Theorem and the Shimura-Taniyama conjecture by A. Wiles and others). Haruzo Hida is Professor of Mathematics at University of California, Los Angeles. His previous books include Modular Forms and Galois Cohomology (Cambridge University Press 2000) and Geometric Modular Forms and Elliptic Curves (World Scientific Publishing Company 2000) Mathematics Geometry, algebraic Number theory Number Theory Algebraic Geometry Mathematik Automorphe Form (DE-588)4003972-9 gnd rswk-swf Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd rswk-swf p-adische Analysis (DE-588)4252360-6 gnd rswk-swf Shimura-Mannigfaltigkeit (DE-588)4181143-4 s Automorphe Form (DE-588)4003972-9 s p-adische Analysis (DE-588)4252360-6 s 1\p DE-604 https://doi.org/10.1007/978-1-4684-9390-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hida, Haruzo p-Adic Automorphic Forms on Shimura Varieties Mathematics Geometry, algebraic Number theory Number Theory Algebraic Geometry Mathematik Automorphe Form (DE-588)4003972-9 gnd Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd p-adische Analysis (DE-588)4252360-6 gnd |
| subject_GND | (DE-588)4003972-9 (DE-588)4181143-4 (DE-588)4252360-6 |
| title | p-Adic Automorphic Forms on Shimura Varieties |
| title_auth | p-Adic Automorphic Forms on Shimura Varieties |
| title_exact_search | p-Adic Automorphic Forms on Shimura Varieties |
| title_full | p-Adic Automorphic Forms on Shimura Varieties by Haruzo Hida |
| title_fullStr | p-Adic Automorphic Forms on Shimura Varieties by Haruzo Hida |
| title_full_unstemmed | p-Adic Automorphic Forms on Shimura Varieties by Haruzo Hida |
| title_short | p-Adic Automorphic Forms on Shimura Varieties |
| title_sort | p adic automorphic forms on shimura varieties |
| topic | Mathematics Geometry, algebraic Number theory Number Theory Algebraic Geometry Mathematik Automorphe Form (DE-588)4003972-9 gnd Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd p-adische Analysis (DE-588)4252360-6 gnd |
| topic_facet | Mathematics Geometry, algebraic Number theory Number Theory Algebraic Geometry Mathematik Automorphe Form Shimura-Mannigfaltigkeit p-adische Analysis |
| url | https://doi.org/10.1007/978-1-4684-9390-0 |
| work_keys_str_mv | AT hidaharuzo padicautomorphicformsonshimuravarieties |