Abstract
In this article, we construct a natural group homomorphismθ:Br(f)→Het1(S,f⁎OX×/OS×) 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.
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