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arXiv · 1208.4447

The derived category analogue of the Hartshorne-Lichtenbaum Vanishing Theorem

Marziyeh Hatamkhani·Kamran Divaani-Aazar
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Abstract

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

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Marziyeh Hatamkhani, Kamran Divaani-Aazar. 2012-08-22. The derived category analogue of the Hartshorne-Lichtenbaum Vanishing Theorem. https://arxiv.org/abs/1208.4447

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