Galois上同调

Foreword

Chapter 1 Cohomology of profinite groups

1. Profinite groups

1.1 Definition

1.2 Subgroups

1.3 Indices

1.4 Pro-p-groups and Sylow p-subgroups

1.5 Pro-p-groups

2 Cohomology

2.1 Discrete G-modules

2.2 Cochains, cocycles, cohomology

2.3 Low dimensions

2.4 Punctoriality

2.5 Induced modules

2.6 Complements

3 Cohomological dimension

3.1 p-cohomological dimension

3.2 Strict cohomological dimension

3.3 Cohomological dimenmon of subgroups and extensions

3.4 Characterization of the profinite groups G such that cdp（G） < 1

3.5 Dualizing modules

4 Cohomology of pro-p-groups

4.1 Simple modules

4.2 Interpretation of Hl: generators

4.3 Interpretation of H2: relations

4.4 A theorem of Shafarevich

4.5 Poincare groups

……

ChapterⅡ Galois cohomology, the commutative case

chapter Ⅲ nonabelian gaiois 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 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. I.H.E.S.， 1965. I am very grateful to him， and to I.H.E.S.， for having authorized this reproduction.