Injectivity of Brauer groups for valuation rings

Abstract: In the non noetherian situation, valuation rings often behave like regular rings. We will discuss several such results which are classically known to be true for regular rings, but also true for valuation rings. We then focus on Brauer groups. It is well known that Br(R) injects into Br(K) provided R is a regular domain and K=qt(R). We observe that the same is true for valuation rings. In fact, we will discuss a more general result in the setting of etale cohomology.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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