# Hélène Esnault

### Algebraic entropy on surfaces

**Abstract**. Hodge theory shows that on a smooth projective over $k=\mathbb{C}$, the maximum of the absolute values of the eigenvalues of an automorphism acting on Betti cohomology is reached on the

N'eron-S\'everi group. That this is so over $k=\mathbb{F}_q$ (replacing Betti by $\ell$-adic cohomology) is a consequence of the standard conjectures (as explained to us by Deligne). We show this property unconditionally. Joint with V. Srinivas.