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p-Adic Automorphic Forms on Shimura Varieties
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2000, ISBN: 9780387207117

In the early years of the 1980s, while I was visiting the Institute for Ad­ vanced Study (lAS) at Princeton as a postdoctoral member, I got a fascinating view, studying congruence modulo … mais…

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Haruzo Hida:

p-Adic Automorphic Forms on Shimura Varieties (Springer Monographs in Mathematics) - encadernado, livro de bolso

2004, ISBN: 0387207112

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Haruzo Hida:
P-Adic Automorphic Forms on Shimura Varieties (Springer Monographs in Mathematics) - encadernado, livro de bolso

2004

ISBN: 9780387207117

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P-Adic Automorphic Forms on Shimura Varieties - Livro de bolso

2004, ISBN: 9780387207117

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P-adic Automorphic Forms on Shimura Varieties - Hida, Haruzo
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Hida, Haruzo:
P-adic Automorphic Forms on Shimura Varieties - encadernado, livro de bolso

2004, ISBN: 0387207112

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P-Adic Automorphic Forms on Shimura Varieties
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Número ISBN:

0387207112


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).

Dados detalhados do livro - P-Adic Automorphic Forms on Shimura Varieties


EAN (ISBN-13): 9780387207117
ISBN (ISBN-10): 0387207112
Livro de capa dura
Livro de bolso
Ano de publicação: 2004
Editor/Editora: SPRINGER NATURE
390 Páginas
Peso: 0,689 kg
Língua: eng/Englisch

Livro na base de dados desde 2007-06-04T19:05:21+01:00 (Lisbon)
Página de detalhes modificada pela última vez em 2024-02-03T08:04:52+00:00 (Lisbon)
Número ISBN/EAN: 0387207112

Número ISBN - Ortografia alternativa:
0-387-20711-2, 978-0-387-20711-7
Ortografia alternativa e termos de pesquisa relacionados:
Autor do livro: hida haruzo, eisenstein, emile borel, poincare, springer
Título do livro: adic, automorphic forms, shimura, shim, automorphic form, springer

Dados da editora

Autor: Haruzo Hida
Título: Springer Monographs in Mathematics; p-Adic Automorphic Forms on Shimura Varieties
Editora: Springer; Springer US
390 Páginas
Ano de publicação: 2004-05-10
New York; NY; US
Língua: Inglês
219,99 € (DE)

BB; Hardcover, Softcover / Mathematik/Arithmetik, Algebra; Zahlentheorie; Verstehen; Grad; algebraic curve; algebraic geometry; deformation theory; modular form; number theory; Number Theory; Algebraic Geometry; Algebraische Geometrie; BC

1 Introduction.- 1.1 Automorphic Forms on Classical Groups.- 1.2 p-Adic Interpolation of Automorphic Forms.- 1.3 p-Adic Automorphic L-functions.- 1.4 Galois Representations.- 1.5 Plan of the Book.- 1.6 Notation.- 2 Geometric Reciprocity Laws.- 2.1 Sketch of Classical Reciprocity Laws.- 2.2 Cyclotomic Reciprocity Laws and Adeles.- 2.3 A Generalization of Galois Theory.- 2.4 Algebraic Curves over a Field.- 2.5 Elliptic Curves over a Field.- 2.6 Elliptic Modular Function Field.- 3 Modular Curves.- 3.1 Basics of Elliptic Curves over a Scheme.- 3.2 Moduli of Elliptic Curves and the Igusa Tower.- 3.3 p-Ordinary Elliptic Modular Forms.- 3.4 Elliptic ?-Adic Forms and p-Adic L-functions.- 4 Hilbert Modular Varieties.- 4.1 Hilbert–Blumenthal Moduli.- 4.2 Hilbert Modular Shimura Varieties.- 4.3 Rank of p-Ordinary Cohomology Groups.- 4.4 Appendix: Fundamental Groups.- 5 Generalized Eichler–Shimura Map.- 5.1 Semi-Simplicity of Hecke Algebras.- 5.2 Explicit Symmetric Domains.- 5.3 The Eichler–Shimura Map.- 6 Moduli Schemes.- 6.1 Hilbert Schemes.- 6.2 Quotients by PGL(n).- 6.3 Mumford Moduli.- 6.4 Siegel Modular Variety.- 7 Shimura Varieties.- 7.1 PEL Moduli Varieties.- 7.2 General Shimura Varieties.- 8 Ordinary p-Adic Automorphic Forms.- 8.1 True and False Automorphic Forms.- 8.2 Deformation Theory of Serre and Tate.- 8.3 Vertical Control Theorem.- 8.4 Irreducibility of Igusa Towers.- References.- Symbol Index.- Statement Index.

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