A cohomological approach to the Brauer-Long group and the groups of Galois extensions and strongly graded rings

Let G be a finite abelian group, and R a commutative ring. The Brauer-Long group BD(R, G) is described by an exact sequence 1 -* BDS(R, G) -* BD(R, G) Aut(G x G*)(R) where BDS (R, G) is a product of etale cohomology groups, and Im fl is a kind of orthogonal subgroup of Aut(G x G*)(R). This sequence generalizes some other well-known exact sequences, and restricts to two split exact sequences describing Galois extensions and strongly graded rings.

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