Open Access
2016 On formal local cohomology modules with respect to a pair of ideals
T.H. Freitas, V.H. Jorge Pérez
J. Commut. Algebra 8(3): 337-366 (2016). DOI: 10.1216/JCA-2016-8-3-337


We introduce a generalization of the formal local cohomology module, which we call a formal local cohomology module with respect to a pair of ideals, and study its various properties. We analyze their structure, upper and lower vanishing and non-vanishing properties. There are various exact sequences concerning formal cohomology modules, among them we have a Mayer-Vietoris sequence with respect to pair ideals. Also, we give another proof for a generalized version of the local duality theorems for Gorenstein, Cohen-Macaulay rings, and a generalization of the Grothendieck duality theorem for Gorenstein rings. We discuss the concept of formal grade with respect to a pair of ideals and give some results about this.


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T.H. Freitas. V.H. Jorge Pérez. "On formal local cohomology modules with respect to a pair of ideals." J. Commut. Algebra 8 (3) 337 - 366, 2016.


Published: 2016
First available in Project Euclid: 9 September 2016

zbMATH: 1348.13026
MathSciNet: MR3546002
Digital Object Identifier: 10.1216/JCA-2016-8-3-337

Primary: 13D45

Keywords: formal local cohomology , local cohomology

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

Vol.8 • No. 3 • 2016
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