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P-Adic Automorphic Forms on Shimura Varieties

Author: Haruzo Hida
Publisher: New York, NY : Springer New York, 2004.
Series: Springer monographs in mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Haruzo Hida
ISBN: 9781468493900 1468493906
OCLC Number: 853267555
Description: 1 online resource (xi, 390 pages).
Contents: Introduction --
Geometric Reciprocity Laws --
Modular Curves --
Hilbert Modular Varieties --
Generalized Eichler-Shimura Map --
Moduli Schemes --
Shimura Varieties --
p-Adic Automorphic Forms --
Bibliography.
Series Title: Springer monographs in mathematics.
Responsibility: by Haruzo Hida.

Abstract:

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).

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From the reviews:"Hida views ... the study of the geometric Galois group of the Shimura tower, as a geometric reciprocity law ... . general goal of the book is to incorporate Shimura's reciprocity Read more...

 
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