Lectures on the Mordell-Weil Theorem
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Jean-Pierre Serre
Lectures on the Mordell-Weil Theorem Third Edition
Jean-Pierre Serre
Lectures on the Mordell-Weil Theorem
Asped~f
Ivbthematia
Edited by Klas Diederich Vol. E 3:
G. Hector/U. Hirsch: Introduction to the Geometry of Foliations, Part B
Vol. E 5:
P. Stiller: Automorphic Forms and the Picard Number of on Elliptic Surface
Vol. E 6:
G. Faltings/G. Wustholz et 01.: Rational Points*
Vol. E 9:
A. Howard/P.-M. Wong (Eds.): Contribution to Several Complex Variables
Vol. E 10: A. J. Tromba (Ed.): Seminar of New Results in Nonlinear Partial Differential Equations * Vol. E 15: J.-P. Serre: lectures on the Mordell-Weil Theorem Vol. E 16: K. Iwasaki/H. Kimura/S. Shimomura/M. Yoshida: From Gauss to Painleve Vol. E 17: K. Diederich lEd.): Complex Analysis Vol. E 18: W. W. J. Hulsbergen: Conjectures in Arithmetic Algebraic Geometry Vol. E 19: R. Rocke: lectures on Nonlinear Evolution Equations Vol. E 20:
F. Hirzebruch, Th. Berger, R. Jung: Manifolds and Modular Forms*
Vol. E 21:
H. Fujimoto: Value Distribution Theory of the Gauss Mop of Minimal Surfaces in Rm
Vol. E 22:
D.
V. Anosov/A. A. Bolibruch: The Riemann-Hilbert Problem
Vol. E 23: A. P. Fordy/J. Vol. E 24:
C. Wood (Eds.): Harmonic Mops and Integrable Systems
D: S. Alexander: A History of Complex Dynamics
Vol. E 25: A. Tikhomirov/A. Tyurin (Eds.): Algebraic Geometry and its Applications Vol. E 26:
H. Skoda/J.-M. Trepreau IEds.): Contributions to Complex Analysis and AnalytiC Geometry
Vol. E 27:
D. N. Akhiezer: lie Group Actions in Complex Analysis
Vol. E 28:
R. Gerard, H. Tahara: Singular Nonlinear Partial Differential Equations
Vol. E 29:
R.-P. Holzapfel: Boll and Surface Arithmetics
Vol. E 30:
R. Huber: Etale Cohomology of Rigid AnalytiC Varieties and Adic Spaces
* A Publication af the Max-Planck-Institut fUr Mathematik,
Bonn
Jean-Pierre Serre
Lectures on the Mordell-Weil Theorem Translated and edited by Martin Brown from notes by Michel Waldschmidt 3rd edition
Springer Fachmedien Wiesbaden GmbH
II Vleweg
Prof. lean-Pierre Serre College de France Chaire d'Algebre et Geometrie 75005 Paris AMS Subject Classification: 14 G 13, 14 K 10, 14 K 15 1st edition 1989 2nd edition 1990 3rd edition 1997
All rights reserved © Springer Fachmedien Wiesbaden 1997 Originally published by Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, BraunschweiglWiesbaden, 1997
No part of this publication may be reproduced, stored in a retrieval system or transmitted, mechanical, photocopying or otherwise, without prior permission of the copyright holder.
Cover design: Wolfgang Nieger, Wiesbaden Printed on acid-free paper ISSN 0179-2156 ISBN 978-3-663-10634-0 DOI 10.1007/978-3-663-10632-6
ISBN 978-3-663-10632-6 (eBook)
v
Foreword
This is a translation of "Autour du theoreme de Mordell-Well", a course given by J.-P. Serre at the College de France in 1980 and 1981. These notes were originally written weekly by Michel Waldschmidt and have been reproduced by Publications Mathematiques de l'Universite de Paris VI, by photocopying the handwritten
