English

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).

Keywords

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

R2 v1 2026-07-22T16:31:00.926Z