%0 Journal Article
%T A finiteness theorem for algebraic cycles
%A Peter O'Sullivan
%J Mathematics
%D 2010
%I arXiv
%X Let X be a smooth projective variety. Starting with a finite set of cycles on powers X^m of X, we consider the Q-vector subspaces of the Q-linear Chow groups of the X^m obtained by iterating the algebraic operations and pullback and push forward along those morphisms X^l -> X^m for which each component X^l -> X is a projection. It is shown that these Q-vector subspaces are all finite-dimensional, provided that the Q-linear Chow motive of X is a direct summand of that of an abelian variety.
%U http://arxiv.org/abs/1003.4789v1