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Article

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

Central European Journal of Mathematics. 2012. Vol. 10. No. 2. P. 559-568.
Gorchinskiy Sergey, Guletskii V.

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.