*p*-Adic Automorphic Forms on Shimura Varieties

Part of the Springer Monographs in Mathematics book series (SMM)

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Part of the Springer Monographs in Mathematics book series (SMM)

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).

Grad algebraic curve algebraic geometry deformation theory modular form number theory

- DOI https://doi.org/10.1007/978-1-4684-9390-0
- Copyright Information Springer-Verlag New York 2004
- Publisher Name Springer, New York, NY
- eBook Packages Springer Book Archive
- Print ISBN 978-1-4419-1923-6
- Online ISBN 978-1-4684-9390-0
- Series Print ISSN 1439-7382
- Buy this book on publisher's site