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arXiv · 1602.03463

On the categorical entropy and the topological entropy

Kohei Kikuta·Atsushi Takahashi
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Abstract

To an exact endofunctor of a triangulated category with a split-generator, the notion of entropy is given by Dimitrov-Haiden-Katzarkov-Kontsevich, which is a (possibly negative infinite) real-valued function of a real variable. In this paper, we propose a conjecture which naturally generalizes the theorem by Gromov-Yomdin, and show that the categorical entropy of a surjective endomorphism of a smooth projective variety is equal to its topological entropy. Moreover, we compute the entropy of autoequivalences of the derived category in the case of the ample canonical or anti-canonical sheaf.

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Kohei Kikuta, Atsushi Takahashi. 2017-07-17. On the categorical entropy and the topological entropy. https://doi.org/10.1093/imrn%2Frnx131

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