arXiv Analytics

Sign in

arXiv:math/0002009 [math.AG]AbstractReferencesReviewsResources

Bloch's Conjecture and Chow Motives

Morihiko Saito

Published 2000-02-01, updated 2000-02-07Version 2

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).

Comments: AMS-TeX, 7 pages; minor change
Categories: math.AG
Subjects: 14C30, 32S35
Related articles: Most relevant | Search more
arXiv:1609.08798 [math.AG] (Published 2016-09-28)
On a multiplicative version of Bloch's conjecture
arXiv:math/9910113 [math.AG] (Published 1999-10-21, updated 2002-11-18)
Bloch's Conjecture, Deligne Cohomology and Higher Chow Groups
arXiv:1510.05832 [math.AG] (Published 2015-10-20)
Bloch's conjecture and valences of correspondences for K3 surfaces

Links

Toolbox