Bloch's Conjecture and Chow Motives
Algebraic Geometry
2007-05-23 v2
Abstract
Let X be a complex surface with no nontrivial 2-forms. Then we show that Bloch's conjecture is true (i.e. the Albanese map in this case is injective) if and only if any homologically trivial idempotent in the ring of correspondences vanishes. Furthermore the cube of the ideal of homologically trivial correspondences is zero if these equivalent conditions are satisfied (e.g. if X is not of general type).
Cite
@article{arxiv.math/0002009,
title = {Bloch's Conjecture and Chow Motives},
author = {Morihiko Saito},
journal= {arXiv preprint arXiv:math/0002009},
year = {2007}
}
Comments
AMS-TeX, 7 pages; minor change