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• W2145252024 startingPage "876" @default.
• W2145252024 abstract "Let $(S, m)$ be an $n$-dimensional regular local ring essentially of finite type over a field and let $I$ be an ideal of $S$. We prove that if $text{depth} S/I ge 3$, then the cohomological dimension $mathrm{cd}(S, I)$ of $I$ is less than or equal to $n-3$. We also show, under the assumption that $S$ has an algebraically closed residue field of characteristic zero, that if $text{depth} S/I ge 4$, then $mathrm{cd}(S, I) le n-4$ if and only if the local Picard group of the completion $widehat{S/I}$ is torsion. We give a number of applications, including sharp bounds on cohomological dimension of ideals whose quotients satisfy good depth conditions such as Serre's conditions $(S_i)$." @default.
• W2145252024 created "2016-06-24" @default.
• W2145252024 creator A5025492010 @default.
• W2145252024 creator A5038445482 @default.
• W2145252024 date "2015-11-03" @default.
• W2145252024 modified "2023-10-03" @default.
• W2145252024 title "On the relationship between depth and cohomological dimension" @default.
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• W2145252024 doi "https://doi.org/10.1112/s0010437x15007678" @default.
• W2145252024 hasPublicationYear "2015" @default.
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