Brauer group and the cohomological Brauer group of schemes.

Time: 16:00-17:45, 26/02/2026 (Thursday)

Venue: Room 612, A6, Institute of Mathematics-VAST

Online (Join Zoom Meeting) link: https://zoom.us/j/99636681387?pwd=0WscBnehOJig68SqctGluVuA3RwraE.1

Abstract: Grothendieck went further by defining the Brauer group of any scheme. The cohomological Brauer group of a quasi-compact scheme X is defined to be the torsion subgroup of the étale cohomology group $H^2(X, G_m)$. The Brauer group is always a subgroup of the cohomological Brauer group.

References:

1. [Gr68] Grothendieck, “Le groupe de Brauer, I-III: Exemples et compléments” in Dix exposés sur la cohomologie des schémas, Adv. Stud. Pure Math. 3, North-Holland, Amsterdam, 1968, 88–188.
2. [Gu12] Guglielmetti, The Brauer-Grothendieck group, Master thesis 2012, https://rgug.ch/medias/math/brauer_grothendieck_group.pdf [Mil80] Milne, Etale cohomology, vol. 33, Princeton Univ Pr, 1980