Functorality of the gamma filtration and computations for some twisted flag varieties

Abstract

We introduce techniques for uniformly studying the gamma filtration of projective homogeneous varieties. These techniques are utilized in some cases of inner-twisted flag varieties (of type A) to show that functorality known for the Chow rings of these varieties also extends to the associated graded rings for the gamma filtrations of the same varieties. As an application, we show that the associated graded groups for the gamma filtration of these varieties are torsion free in low homological degrees.