  In this note we give a closed expression for the number of points over finite
fields of the Lusztig nilpotent variety associated to any quiver without edge
loops, in terms of Kac's A-polynomial. We conjecture a similar result for
quivers in which edge loops are allowed. Finally, we give a formula for the
number of points over a finite field of the various stratas of the Lusztig
nilpotent variety involved in the geometric realization of the crystal graph.
