具有完整局部有限 F 表示类型的环的 F 模块形式主义

Pub Date : 2024-04-02 DOI:10.1093/imrn/rnae054

Eamon Quinlan-Gallego

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引用次数: 0

摘要

我们以柳贝兹尼克和埃默顿-基辛的风格，为在每个素理想处局部化和完备后具有有限 $F$ 表示型的环建立了单位 $F$ 模块的形式主义。作为应用，我们证明如果 $R$ 是这样的环，那么迭代局部同调模块 $H^{n_{1}}_{I_{1}}\cdots \circ H^{n_{s}}_{I_{s}}(R)$ 有有限多个相关素数，并且当 $g$ 是 $R$ 上的非zerodivisor 时，所有局部同调模块 $H^{n}_{I}(R / gR)$ 都有闭支持。

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A Formalism of F-modules for Rings with Complete Local Finite F-Representation Type

We develop a formalism of unit $F$-modules in the style of Lyubeznik and Emerton-Kisin for rings that 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 $R$.

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