Algebraic Cycles and Mumford-Griffiths Invariants

2007/05/31 by James D. Lewis, Lewis, James D., Shuji Saito +1
Mathematics · #14C25 #14C30 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C25 #msc:14C30

paper · pdf · doi:10.48550/arxiv.0705.4661

39 pages, To appear in the American Journal of Mathematics

arxiv created 2007/05/31 · arxiv updated 2009/12/01

Abstract

Let X be a projective algebraic manifold and let CH^r(X) be the Chow group of algebraic cycles of codimension r on X, modulo rational equivalence. Working with a candidate Bloch-Beilinson filtration \F^ν\_{ν≥ 0} on CH^r(X)⊗ \Bbb Q due to the second author, we construct a space of arithmetic Hodge theoretic invariants ∇ J^r,ν(X) and corresponding map ϕ_X^r,ν : Gr_F^νCH^r(X)⊗ \Bbb Q → ∇ J^r,ν(X), and determine conditions on X for which the kernel and image of ϕ_X^r,ν are ``uncountably large''.

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