Relative Brauer groups and etale cohomology

[摘要] In this article, we construct a natural group homomorphism theta : Br(f) -> H-et(1)(S, f(*)O(X)(x)/O-S(X)) for a faithful affine map f : X -> S of noetherian schemes. Here Br(f) denotes the relative Brauer group of f. We also prove Br(f) = 0 whenever f : A -> B is a subintegral extension of noetherian Q-algebras. Furthermore, we prove a relative version of Kummer's exact sequence. (C) 2020 Elsevier B.V. All rights reserved.

[发布日期] 2020-12-01

[关键词] Relative Brauer groups;Subintegral map;Kummer's sequence