A formalism of $F$-modules for rings with complete local finite $F$-representation type
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917611009212416 |
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| author | Quinlan-Gallego, Eamon |
| author_facet | Quinlan-Gallego, Eamon |
| contents | We develop a formalism of unit $F$-modules in the style of Lyubeznik and Emerton-Kisin for rings which have finite $F$-representation type after localization and completion at every prime ideal. As applications, we show that if $R$ is such a ring then the iterated local cohomology modules $H^{n_1}_{I_1} \circ \cdots \circ H^{n_s}_{I_s}(R)$ have finitely many associated primes, and that all local cohomology modules $H^n_I(R / gR)$ have closed support when $g$ is a nonzerodivisor on $R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_02705 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A formalism of $F$-modules for rings with complete local finite $F$-representation type Quinlan-Gallego, Eamon Commutative Algebra Algebraic Geometry We develop a formalism of unit $F$-modules in the style of Lyubeznik and Emerton-Kisin for rings which have finite $F$-representation type after localization and completion at every prime ideal. As applications, we show that if $R$ is such a ring then the iterated local cohomology modules $H^{n_1}_{I_1} \circ \cdots \circ H^{n_s}_{I_s}(R)$ have finitely many associated primes, and that all local cohomology modules $H^n_I(R / gR)$ have closed support when $g$ is a nonzerodivisor on $R$. |
| title | A formalism of $F$-modules for rings with complete local finite $F$-representation type |
| topic | Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/2303.02705 |