Daniel Krashen
Published 2005-01-24, updated 2006-05-13Version 7
In this paper we study the group $A_0(X)$ 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 \'etale subalgebras of central simple algebras which we construct. This allows us to show $A_0(X) = 0$ for certain classes of homogeneous varieties, extending previous results of Swan / Karpenko, of Merkurjev, and of Panin.
Comments: Significant 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
Torsion in Chow groups of zero cycles of homogeneous projective varieties
Zero cycles on certain surfaces in arbitrary characteristic
Automorphism groups of almost homogeneous varieties
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