Galois Theory and Cohomology of Commutative Rings |
Contents
Abelian extensions of commutative rings | 1 |
Galois theory and Galois cohomology of commutative rings | 15 |
Amitsur cohomology and the Brauer group | 33 |
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abelian extension admissible T-isomorphism Alex Rosenberg algebra homomorphism Amer Amitsur cohomology Auslander automorphism Azumaya R-algebra Brauer group category of abelian cl(u cocycle commutative R-algebra commutative ring completes the proof Corollary covariant functor definition denote diagram direct limit direct sum direct summand DOT² elements of G End S's EndA exact sequence exists faithful projective faithfully flat field finite abelian extension finite abelian group finite group finitely generated faithful finitely generated projective follows free R-module Func G-strong Galois cohomology Galois extension Galois group Galois theory group G group homomorphism H(Tot Hence Homp idempotents identity map Math maximal commutative maximal ideal module monomorphism natural transformation naturally isomorphic object of Kp obtain one-one phism prime ideal projective R-module Prop proved R-module of rank R-subalgebra S-algebra isomorphism shows sør² spectral sequence strongly distinct Theorem 1.3 U(S²