Local-global principle for annihilation of general local cohomology

J. Asadollahi ¹   ; K. Khashyarmanesh ²   ; Sh. Salarian ²

¹ School of Science Tarbiat Modarres University P.O. Box 14155-4838 Tehran, Iran
² Institute for Studies in Theoretical Physics and Mathematics P.O. Box 19395-5746 Tehran, Iran and Department of Mathematics Damghan University P.O. Box 36715-364 Damghan, Iran

Colloquium Mathematicum, Tome 87 (2001) no. 1, pp. 129-136

Résumé

Let $A$ be a Noetherian ring, let $M$ be a finitely generated $A$-module and let ${\mit \Phi } $ be a system of ideals of $A$. We prove that, for any ideal ${\mathfrak a}$ in ${\mit \Phi } $, if, for every prime ideal ${\mathfrak p}$ of $A$, there exists an integer $k({\mathfrak p})$, depending on ${\mathfrak p}$, such that ${\mathfrak a}^{k({ \mathfrak p})}$ kills the general local cohomology module $H_{{\mit \Phi } _{{\mathfrak p}}}^j(M_{{ \mathfrak p}})$ for every integer $j$ less than a fixed integer $n$, where ${\mit \Phi } _{{ \mathfrak p}}:=\{ {\mathfrak a}_{{\mathfrak p}}:{\mathfrak a}\in {\mit \Phi } \} $, then there exists an integer $k$ such that ${\mathfrak a}^kH_{{\mit \Phi } }^j(M)=0$ for every $j n$.

Détail

DOI : 10.4064/cm87-1-8

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