Let be a commutative noetherian local ring which is singular and has an isolated singularity. Let be the singularity category of in the sense of Buchweitz and Orlov. In this paper, we find real numbers such that the complexity in the sense of Dimitrov, Haiden, Katzarkov and Kontsevich vanishes for any split generator of and any object of . In particular, the entropy of an exact endofunctor of is not defined for such numbers .
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Ryo Takahashi 1
@article{CRMATH_2023__361_G10_1611_0, 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}, }
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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