Abstract :

Esnault and Srinivas proved that as in de Rham cohomology over the complex numbers, the value of the entropy of an automorphism of a smooth proper surface over a finite field $\mathbb{F}_q$ is taken in the span of the Neron-Severi group inside of $\ell$-adic cohomology. In this talk we will discuss some analogous questions in higher dimensions motivated by their results and techniques.