Algebraic versus topological entropy for surfaces over finite fields

Hélène Esnault, Vasudevan Srinivas

Published 2011-05-12, updated 2011-06-02Version 2

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.