Transcendence degree of zero-cycles and the structure of Chow motives

TL;DR

This paper explores the relationship between the transcendence degree of zero-cycles on smooth projective varieties and the structure of their Chow motives, with implications for Bloch's conjecture, especially for Godeaux surfaces.

Contribution

It establishes a connection between zero-cycle transcendence degrees and the structure of Chow motives, providing new insights into Bloch's conjecture for specific surfaces.

Findings

Transcendence degree relates to Chow motive structure.

Implications for Bloch's conjecture on Godeaux surfaces.

Analysis of zero-cycles on quotients of quintic surfaces.

Abstract

We show how the notion of the transcendence degree of a zero-cycle on a smooth projective variety X is related to the structure of the motive M(X). This can be of particular interest in the context of Bloch's conjecture, especially for Godeaux surfaces, when the surface is given as a finite quotient of a suitable quintic in P^3.