Study on the properties on local cohomology modules from view points of wide cohomology theories

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In the period with the grant, we proved that the category M(R, J)cof of J-cofinite modules is a full sub-category abelian category of the category of all R-modules, provided the ideal J is principal up to radical, where J is an ideal of a noetherian ring R. Further we could give a characterization over regular rings complete with respect to a J-adic topology, after Hartshorne, on the question: when is the complex bounded below J-cofinite?