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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| Main Author: | |
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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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| Summary: | 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 $. |
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| ISSN: | 1778-3569 |