Galois Cohomology

  • Jean-Pierre Serre

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-X
  2. Jean-Pierre Serre
    Pages 1-68
  3. Jean-Pierre Serre
    Pages 69-118
  4. Jean-Pierre Serre
    Pages 119-197
  5. Back Matter
    Pages 199-211

About this book

Introduction

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 bibliography has been extended, open questions have been updated (as far as possible) and several exercises have been added. In order to facilitate references, the numbering of propositions, lemmas and theorems has been kept as in the original 1964 text. Jean-Pierre Serre Harvard, Fall 1996 Table of Contents Foreword ........................................................ V Chapter I. Cohomology of profinite groups §1. Profinite groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . .

Keywords

algebra algebraic geometry group theory number theory algebraic group algebraic number field cohomology field finite group

Authors and affiliations

  • Jean-Pierre Serre
    • 1
  1. 1.Collège de FranceParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-59141-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-42192-4
  • Online ISBN 978-3-642-59141-9
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • About this book
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