Let X be a nonsingular projective variety over the finite field F_q. On the one hand, one can define the zeta function of X. It is a generating function of the numbers of points of X over any finite extensions F_{q^m} of F_q. The famous Weil conjecture is about the properties of this generating function. On the other hand, one can study the bounded derived category of coherent sheaves of X. Orlov has conjectured that derived equivalent smooth, projective varieties have isomorphic motives. It implies that they have the same zeta functions if they are defined over a finite field. In this talk, I will discuss some results on this conjecture and the main references are papers by Katrina Honigs. Speaker(s): Ming Zhang (UM)