Resumen de Motivation for Hodge cycles

Donu Arapura

• Given two smooth projective varieties X and Y, X is defined to motivate Y if the motive of Y is contained in the tensor category generated by X. Some techniques are given for checking this condition. It is shown that in a number of cases moduli spaces of sheaves over curves or surfaces are motivated by the underlying curve or surface. This is used to check the Hodge and related conjectures for some of these examples.