p-Adic Automorphic Forms on Shimura Varieties

Haruzo Hida - Collection Springer Monographs in Mathematics

390 pages, parution le 30/06/2004

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Résumé

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:

An elementary construction of Shimura varieties as moduli of abelian schemes
p-adic deformation theory of automorphic forms on Shimura varieties
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).

Written for:
Graduate math students; research mathematicians

Sommaire

Introduction
Geometric Reciprocity Laws
Modular Curves
Hilbert Modular Varieties
Generalized Eichle
Shimura Map
Moduli Schemes
Shimura Varieties
Adic Automorphic Forms
Bibliography

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	PAPIER
Éditeur(s)	Springer
Auteur(s)	Haruzo Hida
Collection	Springer Monographs in Mathematics
Parution	30/06/2004
Nb. de pages	390
Format	16 x 24
Couverture	Relié
Poids	690g
Intérieur	Noir et Blanc
EAN13	9780387207117
ISBN13	978-0-387-20711-7