Abel-Jacobi Equivalence and a Variant of the Beilinson-Hodge Conjecture

作者：Lewis James D^*

来源：Journal of Mathematical Sciences-The University of Tokyo, 2010, 17(2): 179-199.

• Bloch-Beilinson filtration
• normal function
• Chow group

Let X/C be a smooth projective variety and CHr(X) the Chow group of codimension r algebraic cycles modulo rational equivalence. Let us assume the (conjectured) existence of the Bloch-Beilinson filtration {(FCHr)-C-nu(X) circle times Q}(nu=0)(r) for all such X (and r). If CHAJr (X) subset of CHr(X) is the subgroup of cycles Abel-Jacobi equivalent to zero, then there is an inclusion (FCHr)-C-2(X) circle times Q subset of CG(AJ)(r)(X) circle times Q. Roughly speaking we show that this inclusion is an equality for all X (and r) if and only if a certain variant of Beilinson-Hodge conjecture holds for K-1.

• 出版日期2010