2005/01/24 by Daniel Krashen, Krashen, Daniel · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #14M15 #16K20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation #Rings and Algebras (math.RA) #math.AG #math.RA #msc:14M15 #msc:16K20
paper · pdf · doi:10.48550/arxiv.math/0501399
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
openalex publication_date 2005/01/24 · arxiv created 2006/05/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 for certain classes of homogeneous varieties, extending previous results of Swan / Karpenko, of Merkurjev, and of Panin.