Hartshorne-Lichtenbaum消灭定理的导出范畴类比
The derived category analogue of the Hartshorne-Lichtenbaum Vanishing Theorem
摘要：
设$\fa$是局部环$(R,\fm)$的理想，$X$是$R$ -模的$d$ -维同调有界复形，其所有同调模都是双生成的.我们证明了$H^d_{\fa}(X)=0$当且仅当$\dim \hat{R}/\fa \hat{R}+\fp>0$对$\hat{R}$的所有素理想$\fp$使得$\dim \hat{R}/\fp-\inf (X\otimes_R\hat{R})_{\fp}=d$ .
英文摘要：
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 $\dim \hat{R}/\fp-\inf (X\otimes_R\hat{R})_{\fp}=d$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
