A note on projective dimension over twisted commutative algebras
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866918486385623040 |
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| author | Sam, Steven V Snowden, Andrew |
| author_facet | Sam, Steven V Snowden, Andrew |
| contents | Let $M$ be a finitely generated module over a free twisted commutative algebra $A$ that is finitely generated in degree one. We show that the projective dimension of $M({\bf C}^n)$ as an $A({\bf C}^n)$-module is eventually linear as a function of $n$. This confirms a conjecture of Le, Nagel, Nguyen, and Römer for a special class of modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_05860 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A note on projective dimension over twisted commutative algebras Sam, Steven V Snowden, Andrew Commutative Algebra Let $M$ be a finitely generated module over a free twisted commutative algebra $A$ that is finitely generated in degree one. We show that the projective dimension of $M({\bf C}^n)$ as an $A({\bf C}^n)$-module is eventually linear as a function of $n$. This confirms a conjecture of Le, Nagel, Nguyen, and Römer for a special class of modules. |
| title | A note on projective dimension over twisted commutative algebras |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2207.05860 |