p-Adic Automorphic Forms on Shimura Varieties
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 s
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Haruzo Hida
p-Adic Automorphic Forms on Shimura Varieties
Springer
Haruzo Hida Mathematics Department UCLA Box 951555 Los Angeles, California 90095
Mathematics Subject Classification (2000): llF33, llF41, llF46, llG18, 14G35 Library of Congress Cataloging-in-Publication Data Hida, Haruzo. p-adic automorphic forms on Shimura varieties / Haruzo Hida. p. cm. - (Springer monographs in mathematics) Includes bibliographical references and index. ISBN 978-1-4419-1923-6 ISBN 978-1-4684-9390-0 (eBook) DOI 10.1007/978-1-4684-9390-0 I. Shimura varieties. 2. Automorphic forms. 3. p-adic analysis. QA242.5.H53 2004 515'.9-dc22 ISBN 978-1-4419-1923-6
1. Title.
II. Series.
2003070362
Printed on acid-free paper.
© 2004 Springer-Verlag New York, LLC Softcover repnnt of the hardcover I st editIOn 2004 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, LLC, 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.
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SPIN 10950739
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Preface In the early years of the 1980s, while I was visiting the Institute for Advanced Study (lAS) at Princeton as a postdoctoral member, I got a fascinating view, studying congruence modulo a prime among elliptic modular forms, that an automorphic L-function of a given algebraic group G should have a canonical p-adic counterpart of several variables. I immediately decided to find out the reason behind this phenomenon and to develop the theory of ordinary p-adic automorphic forms, allocating 10 to 15 years from that point, putting off the intended arithmetic study of Shimura varieties via L-functions and Eisenstein series (for which I visited lAS). Although it took more than 15 years, we now know (at least conjecturally) the exact number of variables for a given G, and it has been shown that this is a universal phenomenon valid for holomorphic automorphic forms on Shimura varieties and also for more general (nonholomorphic) cohomological automorphic forms on automorphic manifolds (in a markedly different way). When I was asked to give a series of lectures in the Automorphic Semester in the year 2000 at the Emile Borel Center (Centre Emile Borel) at the Poincare Institute in Paris, I chose to give an exposition of the theory of p-adic (ordinary) families of such automorphic forms p-adic analytically depe
