I am using this page to collect the materials for the 2022 study group on Brauer-Manin Obstructions, co-organised by David Angdinata, Mohammed Alaa Tawfik, and me.
Original proposal/plan for the study group
My notes, which I am trying to update every week
Talks:
Talk 1: Introduction, Mohamed Alaa Tawfik, Notes
Talk 2: The Brauer Group of a Field, Lee Berry
Talk 3: The Brauer Group of a Scheme, Sebastian Monnet
Talk 4 : Examples of Brauer Groups, David Angdinata, Notes
Talk 5: Examples of Purity, Abdulmuhsin Alfaraj, Notes
Talk 6: The Brauer-Manin Set, Tudor Ciurca
References:
'The Brauer-Grothendieck Group'. Book by Colliot-Thelène and Skorobogatov
'Rational Points on Surfaces'. Notes by Bianca Viray from the Arizona Winter School 2015