On an Endomorphism Ring of Local Cohomology

摘要

Let I be an ideal of a local ring (R, ) with d = dim R. For the local cohomology module it is a well-known fact that it vanishes for i > d and is an Artinian R-module for i = d. In the case that the Hartshorne-Lichtenbaum Vanishing Theorem fails, that is we explore its fine structure. In particular, we investigate its endomorphism ring and related connectedness properties. In the case R is complete we prove—as a technical tool—that for a certain ideal J  R. Thus, properties of and its Matlis dual might be described in terms of the local cohomology supported in the maximal ideal.View full textDownload full textKey WordsEndomorphism ring, Hartshorne-Lichtenbaum vanishing theorem, Local cohomology module2000 Mathematics Subject Classification13D45, 13C14Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00927872.2011.588982