math/0501399Jan 24, 2005Significant revisions made to simplify exposition, also includes results for symplectic involution varieties. Main arguments now rely on Hilbert schemes of points and are valid with only mild characteristic assumptions. 32 pages
In this paper we study the group A0(X) of zero dimensional cycles of degree 0 modulo rational equivalence on a projective homogeneous algebraic variety X. To do this we translate rational equivalence of 0-cycles on a projective variety into R-equivalence on symmetric powers of the variety. For certain homogeneous varieties, we then relate these symmetric powers to moduli spaces of étale subalgebras of central simple algebras which we construct. This allows us to show A0(X)=0
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for certain classes of homogeneous varieties, extending previous results of Swan / Karpenko, of Merkurjev, and of Panin.