文档介绍：Progress in Mathematics
Volume 226
Series Editors
Hyman Bass
Joseph Oesterle
Alan Weinstein
Arithmetic of Higher-Dimensional
Algebraic Varieties
Bjorn Poonen
Yuri Tschinkel
Editors
Springer Science+Business Media, LLC
Bjom Poonen Yuri Tschinkel
Department of Mathematics Mathematisches Institut
University of California, Berkeley Bunsenstr. 3-5
Berkeley, CA 94720 D-37073 Gottingen
. Germany
Library of Congress Cataloging-in-Publication Data
A CW catalogue record for this book is available from the Library of Congress,
Washington ., USA.
AMS Subject Classifications: 11045, 11D72, llF72, 11G35, llG50, 11Y50, 14D72, 14E30, 14G05,
14G25
ISBN 978-1-4612-6471-2 ISBN 978-0-8176-8170-8 (eBook) Printed on acid-free paper.
DOI -0-8176-8170-8
***@2004 Springer Science+Business Media New York
Originally published by Birkhauser Boston in 2004
Softcover reprint ofthe hardcover lst edition 2004
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987654321 SPIN 10936412
CONTENTS
Abstracts X l
Introduction xv
Part I. E xpository Articles
SIR P ET ER SWIN NERTON- DvER - Diophantine equations: progress and
problems 3
1. Introduction 3
2. The Hasse Principle and the Brauer- Manin obstruction 6
3. Zeta functions and L-series 12
4. Curves 15
5. Generalities about surfac