Robert Laterveer
Published 2016-09-28Version 1
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.
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
On a multiplicative version of Mumford's theorem
Bloch's conjecture for the surface of Craighero and Gattazzo
Bloch's Conjecture and Chow Motives
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