On the Brauer group and factoriality of normal domains

Abstract

Let B( R) be the Brauer group of the integrally closed noetherian domain R with quotient field K. We reexamine the proof that B( R) → R( K) is monic for R regular from the point of view of factoriality of R and its extensions. For R local with maximal ideal m, henselization R h and divisor class group Cl( R) we embed ker {B(R) → B(K)⊤B( R M )} into Cl(R h) Cl(R) . This is applied to obtain examples of non-regular geometric local domains R for which B( R) → B( K) is monic.