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.