2012/11/21 by Hellus, M., Schenzel, P.
#13D45 (Primary) 14M10 (Secondary) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1211.4956
We provide a formula (see Theorem 1.5) for the Matlis dual of the injective hull of R/\mathfrakp where \mathfrak p is a one dimensional prime ideal in a local complete Gorenstein domain (R,\mathfrakm). This is related to results of Enochs and Xu (see [4] and [3]). We prove a certain 'dual' version of the Hartshorne-Lichtenbaum vanishing (see Theorem 2.2). There is a generalization of local duality to cohomologically complete intersection ideals I in the sense that for I=\mathfrakm we get back the classical Local Duality Theorem. We determine the exact class of modules to which a characterization of cohomologically complete intersection from [6] generalizes naturally (see Theorem 4.4).