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On Shifted Principles for Attached Primes of the Top Local Cohomology Modules

Tran Do Minh Chau , Nguyen Thi Kieu Nga , $icon-email$ Le Thanh Nhan

Abstract

Let $(R, m)$ be a Noetherian local ring, let $I$ be an ideal of $R$ , and let $M$ be a finitely generated $R$ -module with $d = \dim (M)$ . In this paper, we establish shifted principles under localization and completion for attached primes of the top local cohomology module $H_{I}^{d} (M)$ . We characterize the catenarity, the weak going-up property, and the strong Lichstenbaum-Hartshorne vanishing property of the base ring $R$ in terms of these shifted principles of the top local cohomology modules.

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On Shifted Principles for Attached Primes of the Top Local Cohomology Modules

Abstract