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- W2044144614 abstract "Let R be a commutative Noetherian ring, and let $${mathfrak{b} subseteq mathfrak{a}}$$ be ideals of R. The goal of this paper is to show that, for a finitely generated R-module M, if the set $${{rm Ass}_R (H_{mathfrak{a}}^{f_{mathfrak{a}}^{mathfrak{b}}(M)}(M))}$$ is finite or $${f_{mathfrak{a}}(M) neq c_{mathfrak{a}}^{mathfrak{b}}(M)}$$ , then $${f_{mathfrak{a}}^{mathfrak{b}}(M) = {rm inf} {f_{mathfrak{a} R_{mathfrak{p}}}^{mathfrak{b} R_{mathfrak{p}}}(M_{mathfrak{p}})|,,,mathfrak{p} in {rm Spec}(R)}}$$ , where $${c_{mathfrak{a}}^{mathfrak{b}}(M)}$$ denotes the first non $${mathfrak{b}}$$ -cofiniteness of the local cohomology module $${H^i_{mathfrak{a}}(M)}$$ . As a consequence of this, we provide a new and short proof of the Faltings’ local-global principle for finiteness dimensions. Also, several new results concerning the finiteness dimensions are given." @default.
- W2044144614 created "2016-06-24" @default.
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- W2044144614 date "2014-11-13" @default.
- W2044144614 modified "2023-10-07" @default.
- W2044144614 title "A new proof of Faltings’ local-global principle for the finiteness of local cohomology modules" @default.
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- W2044144614 doi "https://doi.org/10.1007/s00013-014-0703-8" @default.
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