Tokyo Journal of Mathematics

The Derived Category Analogue of the Hartshorne-Lichtenbaum Vanishing Theorem


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Let $\mathfrak{a}$ be an ideal of a local ring $(R,\mathfrak{m})$ and $X$ a $d$-dimensional homologically bounded complex of $R$-modules whose all homology modules are finitely generated. We show that $H^d_{\mathfrak{a}}(X)=0$ if and only if $\dim \widehat{R}/\mathfrak{a} \widehat{R}+\mathfrak{p}>0$ for all prime ideals $\mathfrak{p}$ of $\hat{R}$ such that $\dim \hat{R}/\mathfrak{p}-\inf (X\otimes_R\hat{R})_{\mathfrak{p}}=d$.

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Tokyo J. Math., Volume 36, Number 1 (2013), 195-205.

First available in Project Euclid: 22 July 2013

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Zentralblatt MATH identifier

Primary: 13D45: Local cohomology [See also 14B15]
Secondary: 13D02: Syzygies, resolutions, complexes 14B15: Local cohomology [See also 13D45, 32C36]


HATAMKHANI, Marziyeh; DIVAANI-AAZAR, Kamran. The Derived Category Analogue of the Hartshorne-Lichtenbaum Vanishing Theorem. Tokyo J. Math. 36 (2013), no. 1, 195--205. doi:10.3836/tjm/1374497519.

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