Algebra Seminar: Lemire -- Twisted Grassmannians and Torsion in Codimension 2 Chow groups

Nicole Lemire (University of Western Ontario) 

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

Title: Twisted Grassmannians and Torsion in Codimension 2 Chow groups 

Abstract: 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.