  For a proper (not necessarily smooth) variety over a finite field with q
elements, Berthelot-Bloch-Esnault proved a trace formula which computes the
number of rational points modulo q in terms of the Witt vector cohomology. We
show the analogous formula for Witt vector cohomology of finite length. In
addition, we prove a vanishing result for the compactly supported \'etale
cohomology of a constant p-torsion sheaf on an affine Cohen-Macaulay variety in
positive characteristic p.
