TL;DR
This paper proves Bloch's conjecture from 1975, showing that the Albanese kernel of a smooth projective surface is zero when its second cohomology group is algebraic.
Contribution
It provides a proof of Bloch's conjecture, establishing a significant link between the algebraicity of the second cohomology and the Albanese kernel.
Findings
The Albanese kernel is zero under the given conditions.
The conjecture holds for all smooth projective surfaces with algebraic second cohomology.
This result advances understanding of algebraic cycles and surface geometry.
Abstract
We prove the conjecture stated by Spencer Bloch in 1975 and saying that the Albanese kernel of a smooth projective surface is 0, provided its second cohomology group is algebraic.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic Geometry and Number Theory · Geometry and complex manifolds