Sur certains invariants des algèbres artiniennes commutatives
We study properties of algebraic, topological and analytic invariants of commutative artinian algebras and relationships between them. For example, we show that the length of the module of Kähler differentials of any local artinian Gorenstein algebra over $\mathbb{C}$ is greater than or equal to the...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-09-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.589/ |
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| author | Aleksandrov, Alexandre |
| author_facet | Aleksandrov, Alexandre |
| author_sort | Aleksandrov, Alexandre |
| collection | DOAJ |
| description | We study properties of algebraic, topological and analytic invariants of commutative artinian algebras and relationships between them. For example, we show that the length of the module of Kähler differentials of any local artinian Gorenstein algebra over $\mathbb{C}$ is greater than or equal to the length of the algebra itself minus one. We then prove, employing the canonical duality in the cotangent complex, that if the corresponding thick point is smoothable, then its Tjurina and Milnor numbers satisfy the inequality $\tau \geqslant \mu $. |
| format | Article |
| id | doaj-art-87fac2341a824599b8d9bb332d4a0aea |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-87fac2341a824599b8d9bb332d4a0aea2025-02-07T11:22:28ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-09-01362G775175910.5802/crmath.58910.5802/crmath.589Sur certains invariants des algèbres artiniennes commutativesAleksandrov, Alexandre0Institut du Contrôle Automatique de l’Académie des sciences de Russie, 65, rue Profsoyuznaya, GSP-7, Moscou, 117997, Fédération de RussieWe study properties of algebraic, topological and analytic invariants of commutative artinian algebras and relationships between them. For example, we show that the length of the module of Kähler differentials of any local artinian Gorenstein algebra over $\mathbb{C}$ is greater than or equal to the length of the algebra itself minus one. We then prove, employing the canonical duality in the cotangent complex, that if the corresponding thick point is smoothable, then its Tjurina and Milnor numbers satisfy the inequality $\tau \geqslant \mu $.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.589/ |
| spellingShingle | Aleksandrov, Alexandre Sur certains invariants des algèbres artiniennes commutatives Comptes Rendus. Mathématique |
| title | Sur certains invariants des algèbres artiniennes commutatives |
| title_full | Sur certains invariants des algèbres artiniennes commutatives |
| title_fullStr | Sur certains invariants des algèbres artiniennes commutatives |
| title_full_unstemmed | Sur certains invariants des algèbres artiniennes commutatives |
| title_short | Sur certains invariants des algèbres artiniennes commutatives |
| title_sort | sur certains invariants des algebres artiniennes commutatives |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.589/ |
| work_keys_str_mv | AT aleksandrovalexandre surcertainsinvariantsdesalgebresartiniennescommutatives |