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arXiv · 1003.4789

A finiteness theorem for algebraic cycles

Peter O'Sullivan
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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.

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Peter O'Sullivan. 2010-03-25. A finiteness theorem for algebraic cycles. https://arxiv.org/abs/1003.4789

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