Algebraic versus topological entropy for surfaces over finite fields
  We show that, as in de Rham cohomology over the complex numbers, the value of the entropy of an automorphism of the surface over a finite field $\F_q $ is taken on the span of the N\'eron-Severi group inside of $\ell$-adic cohomology. v2: (some) typos removed, exposition (partly) improved. 
H\'el\`ene Esnault and Vasudevan Srinivas
math.AG