Remarks on complexities and entropies for singularity categories

Ryo Takahashi

doi:10.5802/crmath.482

Algèbre

Remarks on complexities and entropies for singularity categories

Ryo Takahashi ¹

¹ Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, Japan

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1611-1623.

Résumé

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 $t$ .

Reçu le : 2022-07-28
Révisé le : 2023-02-02
Accepté le : 2023-02-22
Publié le : 2023-11-17

DOI : 10.5802/crmath.482

Classification : 13D09, 13H10, 18G80

Affiliations des auteurs :

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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     author = {Ryo Takahashi},
     title = {Remarks on complexities and entropies for singularity categories},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1611--1623},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.482},
     language = {en},
}

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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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