Cohomology theories based on Gorenstein injective modules

Asadollahi, Javad; Salarian, Shokrollah

doi:10.1090/S0002-9947-05-03749-9

Cohomology theories based on Gorenstein injective modules
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by Javad Asadollahi and Shokrollah Salarian PDF

Trans. Amer. Math. Soc. 358 (2006), 2183-2203 Request permission

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.

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