Progress in Mathematics Volume 269 Series Editors Hyman Bass Joseph Oesterlé Alan Weinstein For other titles published in this series, go to http://www.springer.com/series/4848 Algebra, Arithmetic, and Geometry In Honor of Yu. I. Manin Volume I Yuri Tschinkel Yuri Zarhin Editors Birkhäuser Boston • Basel • Berlin Editors Yuri Tschinkel Yuri Zarhin New York University Pennsylvania State University Department of Mathematics Eberly College of Science New York, NY 10012-1185 Department of Mathematics
[email protected] University Park, PA 16802
[email protected] ISBN 978-0-8176-4744-5 e-ISBN 978-0-8176-4745-2 DOI 10.1007/978-0-8176-4745-2 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009939499 c Springer Science+Business Media, LLC 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkhäuser Boston, c/o Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly anal- ysis. 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. Printed on acid-free paper Birkhäuser is part of Springer Science+Business Media (www.birkhauser.com) v Preface Yuri Ivanovich Manin has made outstanding contributions to algebra, algebraic geometry, number theory, algorithmic complexity, noncommutative geometry and mathematical physics.