Brauer groups of schemes

Abstract: Topics: Étale cohomology of $\mathbb{G}_m$; definition of cohomological Brauer group of a scheme; Azumaya algebras; definition of Azumaya Brauer group; comparison (without proof).

Reference: Poonen, Rational points on varieties, Section 6.6. See also Colliot-Thélène and Skorobogatov, The Brauer-Grothendieck group, Sections 3.1-3.3 and Chapter 4.

algebraic geometrynumber theory

Audience: advanced learners

STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Spring 2024 topic: The contents of Serre, Lectures on the Mordell-Weil theorem

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.