Congruences for the number of rational points, Hodge type and motivic   conjectures for Fano varieties
  This is meant to be a survey article for the Cubo Journal. We discuss the existence and number of rational points over a finite field, the Hodge type over the complex numbers, and the motivic conjectures which are controlling those invariants. We present a geometric version of it. 
Spencer Bloch and H\'el\`ene Esnault