Brauer groups of fields

Sam Schiavone (MIT)

13-Sep-2022, 15:00-16:30 (18 months ago)

Abstract: Topics: Definition of Brauer group in terms of central simple algebras (also known as Azumaya algebras over a field); definition of Brauer group in terms of Galois cohomology; cyclic algebras; Brauer groups of finite fields, local fields, and global fields (without proofs).

References: Poonen, Rational points on varieties, Section 1.5. See also Gille and Szamuely, Central simple algebras and Galois cohomology, Sections 2.4-2.6, for some of the topics. Also see Milne, Class field theory, Chapter IV and Theorem VIII.4.2.

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.

Organizers: Raymond van Bommel*, Edgar Costa*, Bjorn Poonen*, Shiva Chidambaram*
*contact for this listing

Export talk to