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Finiteness properties of minimax and coatomic local cohomology modules
Arak University.
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
2010 (English)In: ARCHIV DER MATHEMATIK, ISSN 0003-889X, Vol. 94, no 6, 519-528 p.Article in journal (Refereed) Published
Abstract [en]

Let R be a noetherian ring, alpha an ideal of R, and M an R-module. We prove that for a finite module M, if H-alpha(i)(M) is minimax for all i andgt;= r andgt;= 1, then H-alpha(i)(M) is artinian for i andgt;= r. A local-global principle for minimax local cohomology modules is shown. If H-alpha(i)(M) is coatomic for i andlt;= r (M finite) then H-alpha(i)(M) is finite for i andlt;= r. We give conditions for a module which is locally minimax to be a minimax module. A non-vanishing theorem and some vanishing theorems are proved for local cohomology modules.

Place, publisher, year, edition, pages
Springer Science Business Media , 2010. Vol. 94, no 6, 519-528 p.
Keyword [en]
Local cohomology, Minimax module, Coatomic module
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-57419DOI: 10.1007/s00013-010-0127-zISI: 000278347200003OAI: oai:DiVA.org:liu-57419DiVA: diva2:325478
Available from: 2010-06-18 Created: 2010-06-18 Last updated: 2010-06-18

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Melkersson, Leif

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