karpenko at ualberta.ca

Submission: 2017, Apr 18, revised 2017, Oct 21

Let G be a split semisimple algebraic group over an arbitrary field F, let E be a G-torsor over F, and
let P be a parabolic subgroup of G.
The quotient variety X:=E/P, known as a *flag variety*,
is *generically split*, if the parabolic subgroup P is special.
It is *generic*, provided that the G-torsor E over F is a standard generic G'-torsor for
a subfield F' of F and
a split semisimple algebraic group G' over F' with G' over F isomoprhic to G.
For any generically split generic flag variety X,
we show that the Chow ring CH X is generated by Chern classes (of vector bundles over X).
This implies that the topological filtration on the Grothendieck ring of X coincides with the computable gamma filtration.
The results were already known in some cases including the case where P is a Borel subgroup.
We also provide a complete classification of generically split generic flag varieties and, equivalently,
of special parabolic subgroups for split simple groups.

2010 Mathematics Subject Classification: 20G15; 14C25

Keywords and Phrases: Algebraic groups; projective homogeneous varieties; Chow groups.

Full text: dvi.gz 35 k, dvi 82 k, ps.gz 785 k, pdf.gz 181 k, pdf 202 k.

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