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arXiv · 1903.06522

Algebraic entropy for smooth projective varieties

K. V. Shuddhodan
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Abstract

We show that the spectral radius for the action of a self map $f$ of a smooth projective variety (over an arbitrary base field) on its $\ell$-adic cohomology is achieved on the $f^*$-stable sub-algebra generated by any ample class. This generalizes a result of Esnault-Srinivas who had obtained an analogous result for automorphisms of surfaces. Over $\mathbb{C}$ we also show that this sub-algebra is naturally an irreducible representation of a Looijenga-Lunts-Verbitsky type Lie algebra acting on the cohomology of a smooth projective variety.

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K. V. Shuddhodan. 2019-03-15. Algebraic entropy for smooth projective varieties. https://arxiv.org/abs/1903.06522

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