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# 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.

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