On the categorical entropy and the topological entropy
arXiv:1602.03463 · doi:10.1093/imrn/rnx131
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.
11 pages. v2: corrected typos, added explanations in the proof of the main result, v3: added footnotes in page 8
References in corpus (4)
Cited by in corpus (15)
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