By Jean-Pierre Serre

ISBN-10: 3642591418

ISBN-13: 9783642591419

ISBN-10: 364263866X

ISBN-13: 9783642638664

This quantity is an English translation of "Cohomologie Galoisienne" . the unique version (Springer LN5, 1964) used to be according to the notes, written with assistance from Michel Raynaud, of a path I gave on the university de France in 1962-1963. within the current variation there are many additions and one suppression: Verdier's textual content at the duality of profinite teams. crucial addition is the photographic copy of R. Steinberg's "Regular components of semisimple algebraic groups", Publ. Math. LH.E.S., 1965. i'm very thankful to him, and to LH.E.S., for having approved this copy. different additions contain: - an evidence of the Golod-Shafarevich inequality (Chap. I, App. 2). - The "resume de cours" of my 1991-1992 lectures on the collage de France on Galois cohomology of k(T) (Chap. II, App.). - The "resume de cours" of my 1990-1991 lectures on the collage de France on Galois cohomology of semisimple teams, and its relation with abelian cohomology, specifically in size three (Chap. III, App. 2). The bibliography has been prolonged, open questions were up-to-date (as a ways as attainable) and a number of other workouts were further. to be able to facilitate references, the numbering of propositions, lemmas and theorems has been stored as within the unique 1964 textual content. Jean-Pierre Serre Harvard, Fall 1996 desk of Contents Foreword ........................................................ V bankruptcy I. Cohomology of profinite teams §1. Profinite teams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . three . . . . . . . . . . . . . .