On Gromov-Yomdin type theorems and a categorical interpretation of holomorphicity
arXiv:2110.12597
Abstract
In topological dynamics, the Gromov--Yomdin theorem states that the topological entropy of a holomorphic automorphism of a smooth projective variety is equal to the logarithm of the spectral radius of the induced map . In order to establish a categorical analogue of the Gromov--Yomdin 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 Gromov--Yomdin type theorem holds for them.
37 pages. Comments are welcome