On GromovYomdin type theorems and a categorical interpretation of holomorphicity
Abstract
In topological dynamics, the GromovYomdin theorem states that the topological entropy of a holomorphic automorphism $f$ of a smooth projective variety is equal to the logarithm of the spectral radius of the induced map $f^*$. In order to establish a categorical analogue of the GromovYomdin theorem, one first needs to find a categorical analogue of a holomorphic automorphism. In this paper, we propose a categorical analogue of a holomorphic automorphism and prove that the GromovYomdin type theorem holds for them.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 DOI:
 10.48550/arXiv.2110.12597
 arXiv:
 arXiv:2110.12597
 Bibcode:
 2021arXiv211012597B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Category Theory;
 Mathematics  Dynamical Systems
 EPrint:
 37 pages. Comments are welcome