Generation time and algebraic cycles

Generation time was introduced by A. Bondal and M. Van den Bergh in order to demonstrate saturatedness of the derived category of a smooth proper variety. The notion was developed further by R. Rouquier and D. Orlov where they study the minimal generation time and the set of all generation times as a categorical invariant. I will summarize results in a recent preprint with M. Ballard and L. Katzarkov connecting generation time to the existence of algebraic cycles on a smooth variety.