Comptes Rendus
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Remarks on complexities and entropies for singularity categories
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1611-1623.

Let R be a commutative noetherian local ring which is singular and has an isolated singularity. Let D sg (R) be the singularity category of R in the sense of Buchweitz and Orlov. In this paper, we find real numbers t such that the complexity δ t (G,X) in the sense of Dimitrov, Haiden, Katzarkov and Kontsevich vanishes for any split generator G of D sg (R) and any object X of D sg (R). In particular, the entropy h t (F) of an exact endofunctor F of D sg (R) is not defined for such numbers t.

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DOI : 10.5802/crmath.482
Classification : 13D09, 13H10, 18G80

Ryo Takahashi 1

1 Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, Japan
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Ryo Takahashi. Remarks on complexities and entropies for singularity categories. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1611-1623. doi : 10.5802/crmath.482. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.482/

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