Arithmetic and Geometry Papers Dedicated to I.R. Shafarevich on the
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Progress in Mathematics Vol. 35 Edited by J. Coates and S. Helgason
Springer Science+Business Media, LLC
Arithmetic and Geometry Papers Dedicated to I.R. Shafarevich on the Occasion of His Sixtieth Birthday Volume I Arithmetic Michael Artin, John Tate, editors
1983
Springer Science+Business Media, LLC
Editors: Michael Artin Mathematics Department Massachusetts Institute of Technology Cambridge, MA 02139
John Tate Mathematics Department Harvard University Cambridge, MA 02138
This book was typeset at Stanford University using the TEX document preparation system and computer modern type fonts by Y. Kitajima. Special thanks go to Donald E. Knuth for the use of this system and for his personal attention in the development of additional fonts required for these volumes. In addition, we extend thanks to the contributors and editors for their patience and gracious help with implementing this system. Library of Congress Cataloging in Publication Data Main entry under title: Arithmetic and geometry. (Progress in mathematics; v. 35-36) Contents: v. 1. Arithmetic- v. 2. Geometry. 1. Algebra-Addresses, essays, lectures. 2. Geometry, Algebraic-Addresses, essays, lectures. 3. Geometry-Addresses, essays, lectures. 4. Shafarevich, I. R. (Igor' Rostislavovich), 1923I. Shafarevich, I. R. (Igor' Rostislavovich), 1923II. Artin, Michael. Ill. Tate, John Torrence, 1925. IV. Series: Progress in mathematics (Cambridge, Mass.) ; v. 35-36. QA7.A67 1983 513'.132 83-7124 ISBN 978-0-8176-3132-1 ISBN 978-1-4757-9284-3 (eBook) DOI 10.1007/978-1-4757-9284-3
CIP-Kurztitelaufnahme der Deutschen Bibliothek Arithmetic and geometry : papers dedicated to I. R. Shafarevich on the occasion of his 60. birthday I Michael Artin ; John Tate, ed. (Progress in mathematics ; ... ) NE: Artin, Michael (Hrsg.); Safarevic, Igor' R.: Festschrift Vol. 2. Geometry All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior permission of the copyright owner. © Springer Science+Business Media New York 1983 Originally published by Birkhiiuser Boston, Inc., in 1983
ISBN 978-0-8176-3132-1
Igor Rostislavovich Shafarevich has made outstanding contributions in number theory, algebra, and algebraic geometry. The flourishing of these fields in Moscow since World War II owes much to his influence. We hope these papers, collected for his sixtieth birthday, will indicate to him the great respect and admiration which mathematicians throughout the world have for him. Michael Artin Igor Dolgachev John Tate A.N. Todorov
I.R. Shafarevich, Moscow, 1966
Volume I Arithmetic N. Aoki and T. Shioda, Generators of the Neron-Severi Group of a Fermat Surface
1
S. Bloch, p-adic Etale Cohomology
13
J. W .S. Cassels, The Mordell-Weil Group of Curves of Genus 2
27
G.V. Chudnovsky, Number Theoretic Applications of Polynomials with Rational Coefficients Defined by Extremality Conditions
61
J. Coates, Infinite Descent on
