In this note we present some results on the Chow motive h(X) of an algebraic surface X and relate them to the conjectures of Bloch, Beilinson and Murre. In particular we illustrate the relations between the finite-dimensionality of h(X) and the geometric properties of the surface. Then we focus on the case, where the conjectures are still open, of a complex K3 surface and prove some results which give some evidence to the finite-dimensionality of h(X).
The Chow Motive of a K3 Surface
PEDRINI, CLAUDIO
2009-01-01
Abstract
In this note we present some results on the Chow motive h(X) of an algebraic surface X and relate them to the conjectures of Bloch, Beilinson and Murre. In particular we illustrate the relations between the finite-dimensionality of h(X) and the geometric properties of the surface. Then we focus on the case, where the conjectures are still open, of a complex K3 surface and prove some results which give some evidence to the finite-dimensionality of h(X).
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