Mittag-Leffler modules and variants on intersection flatness
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913773401407488 |
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| author | Datta, Rankeya Epstein, Neil Tucker, Kevin |
| author_facet | Datta, Rankeya Epstein, Neil Tucker, Kevin |
| contents | We systematically study the intersection flatness and Ohm-Rush properties for modules over a commutative ring, drawing inspiration from the work of Ohm and Rush and of Hochster and Jeffries. We establish new structural results for modules that are intersection flat/Ohm-Rush by exhibiting intimate connections between these notions and the seminal work of Raynaud and Gruson on Mittag-Leffler modules. In particular, we develop a theory of Ohm-Rush modules that is parallel to the theory of Mittag-Leffler modules. We also obtain descent and local-to-global results for intersection flat/Ohm-Rush modules. Our investigations reveal a particularly pleasing picture for flat modules over a complete local ring, in which case many otherwise distinct properties coincide. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_11139 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mittag-Leffler modules and variants on intersection flatness Datta, Rankeya Epstein, Neil Tucker, Kevin Commutative Algebra Algebraic Geometry 13C05, 13C11, 13C13, 13H05, 13B35, 13F40 We systematically study the intersection flatness and Ohm-Rush properties for modules over a commutative ring, drawing inspiration from the work of Ohm and Rush and of Hochster and Jeffries. We establish new structural results for modules that are intersection flat/Ohm-Rush by exhibiting intimate connections between these notions and the seminal work of Raynaud and Gruson on Mittag-Leffler modules. In particular, we develop a theory of Ohm-Rush modules that is parallel to the theory of Mittag-Leffler modules. We also obtain descent and local-to-global results for intersection flat/Ohm-Rush modules. Our investigations reveal a particularly pleasing picture for flat modules over a complete local ring, in which case many otherwise distinct properties coincide. |
| title | Mittag-Leffler modules and variants on intersection flatness |
| topic | Commutative Algebra Algebraic Geometry 13C05, 13C11, 13C13, 13H05, 13B35, 13F40 |
| url | https://arxiv.org/abs/2305.11139 |