On liftings of modules of finite projective dimension
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917828435640320 |
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| author | KC, Nawaj Levins, Andrew J. Soto |
| author_facet | KC, Nawaj Levins, Andrew J. Soto |
| contents | We introduce and study a notion of Serre liftable modules; these are modules that are liftable to modules of the maximal possible dimension over a regular local ring. We establish new cases of Serre's positivity conjecture over ramified regular local rings by proving it for Serre liftable modules. Furthermore, we show that the length of a nonzero Serre liftable module is bounded below by the Hilbert-Samuel multiplicity of the local ring. This establishes special cases of the Length Conjecture of Iyengar-Ma-Walker. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17572 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On liftings of modules of finite projective dimension KC, Nawaj Levins, Andrew J. Soto Commutative Algebra We introduce and study a notion of Serre liftable modules; these are modules that are liftable to modules of the maximal possible dimension over a regular local ring. We establish new cases of Serre's positivity conjecture over ramified regular local rings by proving it for Serre liftable modules. Furthermore, we show that the length of a nonzero Serre liftable module is bounded below by the Hilbert-Samuel multiplicity of the local ring. This establishes special cases of the Length Conjecture of Iyengar-Ma-Walker. |
| title | On liftings of modules of finite projective dimension |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2404.17572 |