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Cohomology theories based on Gorenstein injective modules |
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| Authors: | Javad Asadollahi Shokrollah Salarian |
| Affiliation: | School of Mathematics, Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5746, Tehran, Iran -- and -- Shahre-Kord University, P.O. Box 115, Shahre-Kord, Iran ; School of Mathematics, Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5746, Tehran, Iran -- and -- Department of Mathematics, University of Isfahan, P.O. Box 81746-73441, Isfahan, Iran |
| Abstract: | In this paper we study relative and Tate cohomology of modules of finite Gorenstein injective dimension. Using these cohomology theories, we present variations of Grothendieck local cohomology modules, namely Gorenstein and Tate local cohomology modules. By applying a sort of Avramov-Martsinkovsky exact sequence, we show that these two variations of local cohomology are tightly connected to the generalized local cohomology modules introduced by J. Herzog. We discuss some properties of these modules and give some results concerning their vanishing and non-vanishing. |
| Keywords: | Gorenstein injective coresolutions local cohomology modules Tate cohomology Gorenstein rings Gorenstein dimension |
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