Mathematical Proceedings of the Cambridge Philosophical Society



Ideal topologies, local cohomology and connectedness


K. DIVAANI-AAZAR a1 1 and P. SCHENZEL a2
a1 Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-1795, Tehran, Iran. e-mail: kdevania@rose.ipm.ac.ir
a2 Martin-Luther-Universität Halle-Wittenberg, Fachbereich Mathematik und Informatik, D–06 099 Halle (Saale), Germany. e-mail: schenzel@mathematik.uni-halle.de

Abstract

Let [fraktur a] be an ideal of a local ring (R, [fraktur m]) and let N be a finitely generated R-module of dimension d: It is shown that Hd[fraktur a](N) [simeq R: similar, equals] Hd[fraktur m](N)/[sum L: summation operator]n[set membership][open face N][left angle bracket][fraktur m][right angle bracket] (0: Hd[fraktur m](N)[fraktur a]n); where for an Artinian R-module X we put [left angle bracket][fraktur m][right angle bracket]X = [cap B: intersection]n[set membership][open face N][fraktur m]nX. As a consequence several vanishing and connectedness results are deduced.

(Received November 25 1999)
(Revised April 6 2000)



Footnotes

1 The first named author was partially supported by the Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran.