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- W2015180666 abstract "Let R be a commutative Noetherian ring, $${{mathfrak{a}}}$$ an ideal of R, and let M be a finitely generated R-module. For a non-negative integer t, we prove that $$H_{mathfrak{a}}^t(M)$$ is $${{mathfrak{a}}}$$ -cofinite whenever $$H_{mathfrak{a}}^t(M)$$ is Artinian and $$H_{mathfrak{a}}^i(M)$$ is $${{mathfrak{a}}}$$ -cofinite for all i < t. This result, in particular, characterizes the $${{mathfrak{a}}}$$ -cofiniteness property of local cohomology modules of certain regular local rings. Also, we show that for a local ring $$(R,{{mathfrak{m}}})$$ , f – $$hbox{depth}(mathfrak{a},M)$$ is the least integer i such that $$H^{i}_{mathfrak{a}} (M) ncong H^{i}_{{mathfrak{m}}} (M)$$ . This result, in conjunction with the first one, yields some interesting consequences. Finally, we extend Grothendieck’s non-vanishing Theorem to $${{mathfrak{a}}}$$ -cofinite modules." @default.
- W2015180666 created "2016-06-24" @default.
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- W2015180666 date "2006-09-01" @default.
- W2015180666 modified "2023-10-06" @default.
- W2015180666 title "Some results on local cohomology modules" @default.
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- W2015180666 doi "https://doi.org/10.1007/s00013-006-1674-1" @default.
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