Basic Number Theory
)tPI(}jlOV, e~oxov (10CPUljlr1.'CWV Aiux., llpop. . .dsup.. The first part of this volume is based on a course taught at Princeton University in 1961-62; at that time, an excellent set of notes was prepared by David Cantor, and it was originally my intent
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Classics in Mathematics Andre Weil Basic Number Theory
Andre Weil
Basic Number Theory Reprint of the 1974 Edition
Springer
Andre Wei! Institute for Advanced Study Princeton. NJ 08540 USA
Originally published as Vol. 144 of the
Grundlehren der mathematischen Wissenschaften
Mathematics Subject Classification (1991): llR
ISBN-13: 978-3-540-58655-5 DOl: 10.1007/978-3-642-61945-8
e-ISBN-13: 978-3-642-61945-8
Photograph by kind permission of Lucien Gillet
elP data applied for This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned. specifically the rights of translation. reprinting. reuse of illustration, recitation. broadcasting. reproduction on microfilm or in any other way. and storase in data banks. Duplication of this publication or parts thereof is permitted only under the provision of the German Copyright Law of September 9. 1965. in its current version. and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under tbe German Copyright Law. @Springer-VerlasBerIinHeideiberg 1995 The use of general descriptive names, registered names. trademarks. etc. in this publication does not imply. even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
SPIN 10701941
4113111 - 5 4 3 21 - Printed on acid-free paper
Andre Weil
Basic Number Theory
Third Edition 1974
Springer-Verlag Berlin • Heidelberg • New York 1974
Professor Andre Weil The Institute for Advanced Study, Princeton, N. J. 08540
All rights, especially that of translation into foreign languages, reserved. It. is also forbidden to reproduce this book, either whole or in part, by photomechanical means (photostat, microfilm and/or microcard) or by other procedure without written permission from Springer-Verlag © 1973 by Springer-Verlag New York Inc.
Library of Congress Catalog Card Number 73-75018
Foreword )tPI(}jlOV, e~oxov (10CPUljlr1.'CWV
Aiux., llpop.. .dsup..
The first part of this volume is based on a course taught at Princeton University in 1961-62; at that time, an excellent set of notes was prepared by David Cantor, and it was originally my intention to make these notes available to the mathematical public with only quite minor changes. Then, among some old papers of mine, I accidentally came across a long-forgotten manuscript by Chevalley, of pre-war vintage (forgotten, that is to say, both by me and by its author) which, to my taste at least, seemed to have aged very well. It contained a brief but essentially complete account of the main features of classfield theory, both local and global; and it soon became obvious that the usefulness of the intended volume would be greatly enhanced if I included such a treatment of this topic. It had to be expanded, in accordance with my own plans, but its outline could be preserved without much change. In fact, I have adhered to it rather closely at some critical points. To improve upo
