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OverviewThis 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 . . . . . . . . . . . . . . Full Product DetailsAuthor: Jean-Pierre Serre , P. IonPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: Softcover reprint of the original 1st ed. 1997 Dimensions: Width: 15.50cm , Height: 1.20cm , Length: 23.50cm Weight: 0.349kg ISBN: 9783642638664ISBN 10: 364263866 Pages: 212 Publication Date: 16 November 2012 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsI. Cohomology of profinite groups.- §1. Profinite groups.- §2. Cohomology.- §3. Cohomological dimension.- §4. Cohomology of pro-p-groups.- §5. Nonabelian cohomology.- II. Galois cohomology, the commutative case.- §1. Generalities.- §2. Criteria for cohomological dimension.- §3. Fields of dimension ?1.- §4. Transition theorems.- §5. p-adic fields.- §6. Algebraic number fields.- III. Nonabelian Galois cohomology.- §1. Forms.- §2. Fields of dimension ? 1.- §3. Fields of dimension ? 2.- §4. Finiteness theorems.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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