LOCAL HOMOLOGY AND GORENSTEIN FLAT MODULES

Let R be a commutative Noetherian ring, a be an ideal of R and D(R) denote the derived category of R-modules. We investigate the theory of local homology in conjunction with Gorenstein flat modules. Let X be a homologically bounded to the right complex and Q be a bounded to the right complex of Gorenstein flat R-modules such that Q and X are isomorphic in D(R). We establish a natural isomorphism L Lambda(a)(X) similar or equal to Lambda(a)(Q) in D(R) which immediately asserts that sup L Lambda(a)(X) <= Gfd(R) X. This isomorphism yields several consequences. For instance, in the case R possesses a dualizing complex, we show that Gfd(R) L Lambda(a)(X) <= Gfd(R) X. Also, we establish a criterion for regularity of Gorenstein local rings.