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Ideal topologies, local cohomology and connectedness

Published online by Cambridge University Press:  26 October 2001

K. DIVAANI-AAZAR  and
P. SCHENZEL
K. DIVAANI-AAZAR
Affiliation:
Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-1795, Tehran, Iran. e-mail: [email protected]
P. SCHENZEL
Affiliation:
Martin-Luther-Universität Halle-Wittenberg, Fachbereich Mathematik und Informatik, D–06 099 Halle (Saale), Germany. e-mail: [email protected]
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Abstract

Let [afr ] be an ideal of a local ring (R, [mfr ]) and let N be a finitely generated R-module of dimension d: It is shown that Hd[afr ](N) ≃ Hd[mfr ](N)/[sum ]n∈ℕ〈[mfr ]〉 (0: Hd[mfr ](N)[afr ]n); where for an Artinian R-module X we put 〈[mfr ]〉X = ∩n∈ℕ[mfr ]nX. As a consequence several vanishing and connectedness results are deduced.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 131 , Issue 2 , September 2001 , pp. 211 - 226
Copyright
2001 Cambridge Philosophical Society

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