Relative Brauer Groups and étale cohomology

2019/06/26 by Sadhu, Vivek
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.10846

Abstract

In this article, we construct a natural group homomorphism ψ: Br(f)→ H¹_et(S, f_*O_X^×/O_S^×) for a faithful affine map f: X → S of noetherian schemes. Here Br(f) denotes the relative Brauer group of f. We also discuss the behavior of Brauer groups for a subintegral map. Furthermore, we prove a relative version of Kummer's exact sequence.

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