English

On a multiplicative version of Bloch's conjecture

Algebraic Geometry 2016-09-29 v1

Abstract

A theorem of Esnault, Srinivas and Viehweg asserts that if the Chow group of 0-cycles of a smooth complete complex variety decomposes, then the top-degree coherent cohomology group decomposes similarly. In this note, we prove that (a weak version of) the converse holds for varieties of dimension at most 5 that have finite-dimensional motive and satisfy the Lefschetz standard conjecture. The proof is based on Vial's construction of a refined Chow-Kunneth decomposition for these varieties.

Keywords

Cite

@article{arxiv.1609.08798,
  title  = {On a multiplicative version of Bloch's conjecture},
  author = {Robert Laterveer},
  journal= {arXiv preprint arXiv:1609.08798},
  year   = {2016}
}

Comments

To appear (in slightly different form) in Beitrage zur Algebra und Geometrie, 8 pages, comments welcome. arXiv admin note: text overlap with arXiv:1602.04944

R2 v1 2026-06-22T16:03:49.643Z