Rees algebras and generalized depth-like conditions in prime characteristic
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866910481370841088 |
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| author | Costantini, Alessandra Maddox, Kyle Miller, Lance Edward |
| author_facet | Costantini, Alessandra Maddox, Kyle Miller, Lance Edward |
| contents | In this article we address a question concerning nilpotent Frobenius actions on Rees algebras and associated graded rings. We prove a nilpotent analog of a theorem of Huneke for Cohen-Macaulay singularities. This is achieved by introducing a depth-like invariant which captures as special cases Lyubeznik's F-depth and the generalized F-depth from Maddox-Miller and is related to the generalized depth with respect to an ideal. We also describe several properties of this new invariant and identify a class of regular elements for which weak F-nilpotence deforms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2212_11374 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rees algebras and generalized depth-like conditions in prime characteristic Costantini, Alessandra Maddox, Kyle Miller, Lance Edward Commutative Algebra 13A35 (Primary) 13A30, 13D45, 13H10 (Secondary) In this article we address a question concerning nilpotent Frobenius actions on Rees algebras and associated graded rings. We prove a nilpotent analog of a theorem of Huneke for Cohen-Macaulay singularities. This is achieved by introducing a depth-like invariant which captures as special cases Lyubeznik's F-depth and the generalized F-depth from Maddox-Miller and is related to the generalized depth with respect to an ideal. We also describe several properties of this new invariant and identify a class of regular elements for which weak F-nilpotence deforms. |
| title | Rees algebras and generalized depth-like conditions in prime characteristic |
| topic | Commutative Algebra 13A35 (Primary) 13A30, 13D45, 13H10 (Secondary) |
| url | https://arxiv.org/abs/2212.11374 |