On Gromov–Yomdin type theorems and a categorical interpretation of holomorphicity

Federico Barbacovi ^[1] ; Jongmyeong Kim ^[2]
1. [1] University College London
  
  University College London
  
  Reino Unido
2. [2] Institute for Basic Science (IBS), Corea del Sur
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 4, 2023
Idioma: inglés
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Resumen
- In topological dynamics, the Gromov–Yomdin 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 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.