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arXiv · 1609.08798

On a multiplicative version of Bloch's conjecture

Robert Laterveer
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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.

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Robert Laterveer. 2016-09-28. On a multiplicative version of Bloch's conjecture. https://doi.org/10.1007/s13366-016-0296-4

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