Galois Cohomology
This volume is an English translation of "Cohomologie Galoisienne" . The original edition (Springer LN5, 1964) was based on the notes, written with the help of Michel Raynaud, of a course I gave at the College de France in 1962-1963. In the present editio
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Springer-Verlag Berlin Heidelberg GmbH
Jean-Pierre Serre
Galois Cohomology Translated from the French by Patrick Ion
,
Springer
]ean-Pierre Serre College de France 3 rued'Ulm 75005 Paris France e-mail: [email protected]
Patrick ion (Translator) Mathematical Reviews P. O. Box 8604 Ann Arbor, MI 48017-8604 USA
Library of Congress Cataloging-in-Publication Data applied for Die Deutache Bibliothek - C1P-Einheitsaufnahme SerIe. Jean-Pierre: Galois cohomology I Jean-Pierre Serre. Transl. from the French by Patrick Ion. Corr. 2. printing. - Berlin; Heide1berg ; New York; Barcelona ; Hong Kong ; London ; MUan ; Paris ; Tokyo : Springer. 2002 (Springer monographs in mathematics) Einheitssacht.: Cohomologie galoisienne
ISBN 978-3-642-63866-4 DOI 10.1007/978-3-642-59141-9
ISBN 978-3-642-59141-9 (eBook)
Corrected Second Printing 2002 of the First English Edition of 1997
Mathematics Subject Classification (2000): 12B20
ISSN 1439-7382 ISBN 978-3-642-63866-4 ThiI work is subject to copyright AU righu are reserved, whether the whole or part of the material is concerned. specifica\lythe rightl oftranslation. reprinting. reuse ofillustrationl.recitation. broadcasting, reproduction on microfilm or in any other way. and storage in data banks. Duplication of this publication or parts thereof is permitted on1y under the provisions of the German Copyright Law of September 9. 1965. in its current version. and permission for use must a1ways be obtained from Springer-Verl.g. Violations are Iiable for prosecution under the German Copyright Law.
http://WWW.springer.de © Springer-ver\ag BerIio Heidelberg 1997 OriginaJ\ypub\ishedby Springer-Ver\ag BerIio Heidelberg New York in 1997 The use of general descriptive names. registered names. trademarks. etc. in this publication doel not inlply. even in the absence of a specific statement. that such namel are exempt from the relevant protective Iaws and regu1ations and therefore free for general use. SPIN: 10841416
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Foreword
This volume is an English translation of "Cohomologie Galoisienne" . The original edition (Springer LN5, 1964) was based on the notes, written with the help of Michel Raynaud, of a course I gave at the College de France in 1962-1963. In the present edition there are numerous additions and one suppression: Verdier's text on the duality of profinite groups. The most important addition is the photographic reproduction of R. Steinberg's "Regular elements of semisimple algebraic groups", Publ. Math. LH.E.S., 1965. I am very grateful to him, and to LH.E.S., for having authorized this reproduction. Other additions include: - A proof of the Golod-Shafarevich inequality (Chap. I, App. 2). - The "resume de cours" of my 1991-1992 lectures at the College de France on Galois cohomology of k(T) (Chap. II, App.). - The "resume de cours" of my 1990-1991 lectures at the College de France on Galois cohomology of semisimple groups, and its relation with abelian cohomology, especially in dimension 3 (Chap. III, App. 2). The bibli
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