p-Adic Automorphic Forms on Shimura Varieties
By: by Haruzo Hida
Series: Springer Monographs in Mathematics; Springer monographs in mathematics
Publisher: Springer New York
Published: 2004
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 390
ISBN-13: 9781441919236; 9781468493900
Subjects: Mathematics; Algebraic Geometry; Number theory
Description: 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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Table of contents: title: Introduction; title: Geometric Reciprocity Laws; title: Modular Curves; title: Hilbert Modular Varieties; title: Generalized Eichler-Shimura Map; title: Moduli Schemes; title: Shimura Varieties; title: p-Adic Automorphic Forms; title: Bibliography.