A higher algebraic approach to liftings of modules over derived quotients
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909556976648192 |
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| author | Ishizuka, Ryo |
| author_facet | Ishizuka, Ryo |
| contents | We show a certain existence of a lifting of modules under the self-$\mathrm{Ext}^2$-vanishing condition over the "derived quotient" by using the notion of higher algebra. This refines a work of Auslander-Ding-Solberg's solution of the Auslander-Reiten conjecture for complete interesctions. Together with Auslander's zero-divisor theorem, we show that the existence of such $\mathrm{Ext}$-vanishing module over derived quotients is equivalent to being local complete intersections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17964 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A higher algebraic approach to liftings of modules over derived quotients Ishizuka, Ryo Commutative Algebra Number Theory Rings and Algebras We show a certain existence of a lifting of modules under the self-$\mathrm{Ext}^2$-vanishing condition over the "derived quotient" by using the notion of higher algebra. This refines a work of Auslander-Ding-Solberg's solution of the Auslander-Reiten conjecture for complete interesctions. Together with Auslander's zero-divisor theorem, we show that the existence of such $\mathrm{Ext}$-vanishing module over derived quotients is equivalent to being local complete intersections. |
| title | A higher algebraic approach to liftings of modules over derived quotients |
| topic | Commutative Algebra Number Theory Rings and Algebras |
| url | https://arxiv.org/abs/2503.17964 |