On vanishing of unramified cohomology of geometrically rational   varieties over finite fields
  The purpose of this paper is to show that the third unramified cohomology with divisible coefficients of a smooth projective geometrically rational threefold over a finite field must vanish under $\Z_{\ell}$-exactness Hard Lefschetz condition. 
Nguyen Le Dang Thi
math.AG