A finiteness theorem for algebraic cycles
Algebraic Geometry
2010-03-26 v1
Abstract
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.
Cite
@article{arxiv.1003.4789,
title = {A finiteness theorem for algebraic cycles},
author = {Peter O'Sullivan},
journal= {arXiv preprint arXiv:1003.4789},
year = {2010}
}
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20 pages