University of Sydney Algebra Seminar

Nicole Lemire (University of Western Ontario)

Friday 10 March, 2:30-3:30pm, Place: Carslaw 375

Twisted Grassmannians and Torsion in Codimension 2 Chow groups

Twisted projective homogeneous varieties for algebraic groups are projective varieties which are isomorphic to a given projective homogeneous variety after extension to the separable closure of the field. Important examples include Severi Brauer varieties, which are twisted forms of projective space; generalised Severi Brauer varieties, which are twisted forms of Grassmannians. We determine necessary and sufficient conditions under which generalised Severi Brauer varieties have rational subvarieties which are forms of given Schubert subvarieties of the associated Grassmannian. Using a motivic decomposition of the motive of the generalised Severi Brauer variety, we show that the codimension 2 Chow groups of certain generalised Severi Brauer varieties are torsion free. This is joint work with Caroline Junkins and Danny Krashen.