Algebraic Brauer groups modulo constants of homogeneous spaces

par Manh Linh Nguyen

jeudi 23 juin 2022, 14:00 → 15:00 Europe/Paris

M7.411 (ENS Lyon, UMPA)

For a homogeneous space of a semisimple, simply connected linear algebraic group, the quotient of its "unramified algebraic" Brauer group by its subgroup of constants injects into a certain subgroup of the first Galois cohomology of its geometric Picard group. This inclusion is an isomorphism if either the homogeneous space has a rational point or the third Galois cohomology of the multiplicative group over the base field vanishes. In my talk, I construct an example where this inclusion is strict. This is the text https://arxiv.org/abs/2204.10967.