On a multiplicative version of Bloch's conjecture

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.

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

Cited by in corpus (1)

• Zero-cycles on self-products of surfaces: some new examples verifying Voisin's conjecture