p-Adic Automorphic Forms on Shimura Varieties - Rilegato

Hida, Haruzo

Rilegato

ISBN 10: 0387207112 ISBN 13: 9780387207117

Casa editrice: Springer-Verlag GmbH, 2004

Riassunto

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 schemes2. p-adic deformation theory of automorphic forms on Shimura varieties3. A simple proof of irreducibility of the generalized Igusa tower over the Shimura varietyThe 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).

Su questo libro

Dalla quarta di copertina

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).

Dettagli dell'edizione

• Editore: Springer-Verlag GmbH
• Data di pubblicazione: 2004
• Lingua: Inglese
• ISBN 10: 0387207112
• ISBN 13: 9780387207117
• Rilegatura: Copertina rigida
• Numero di pagine: 390
• Contatto del produttore: Elevation; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; 22391; Germania