Bloch's Conjecture, Deligne Cohomology and Higher Chow Groups
| dc.creator | Saito, Morihiko | |
| dc.date | 1999-10-21 | |
| dc.date | 2002-11-18 | |
| dc.date.accessioned | 2026-07-07T05:31:14Z | |
| dc.date.available | 2026-07-07T05:31:14Z | |
| dc.description | We express the kernel of Griffiths' Abel-Jacobi map by using the inductive limit of Deligne cohomology in the generalized sense (i.e. the absolute Hodge cohomology of A. Beilinson). This generalizes a result of L. Barbieri-Viale and V. Srinivas in the surface case. We then show that the Abel-Jacobi map for codimension 2 cycles and the Albanese map are bijective if a general hyperplane section is a surface for which Bloch's conjecture is proved. In certain cases we verify Nori's conjecture on the Griffiths group. We also prove a weak Lefschetz-type theorem for (higher) Chow groups, generalize a formula for the Abel-Jacobi map of higher cycles due to Beilinson and Levine to the smooth non proper case, and give a sufficient condition for the nonvanishing of the transcendental part of the image by the Abel-Jacobi map of a higher cycle on an elliptic surface, together with some examples. | |
| dc.description | 33 pages, the bijectivity of the Albanese map is treated in (0.4), and a weak Lefschetz-type theorem for (higher) Chow groups is studied | |
| dc.identifier | https://arxiv.org/abs/math/9910113 | |
| dc.identifier | http://arxiv.org/abs/math/9910113 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79270 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14C30, 32S35 | |
| dc.title | Bloch's Conjecture, Deligne Cohomology and Higher Chow Groups | |
| dc.type | text |