Complexes of Cousin type and modules of generalized fractions

Abstract

Let R be a commutative (Noetherian) ring, M an R-module and let ℱ = (Fi)i≥0 be a filtration of Spec(R) which admits M.A complex of R-modules is said to be of Cousin type if it satisfies the four conditions of ([GO], 3.2) which are reproduced below (Definition (1.5)). In ([RSZ], 3.4), Riley, Sharp and Zakeri proved that the complex, which is constructed from a chain of special triangular subsets defined in terms of ℱ (Example (1.3)(3)), is of Cousin type for M with respect to ℱ (Corollary (3.5)(2)). Gibson and O’carroll ([GO], 3.6) showed that the complex, which is obtained by means of a chain = (Ui)i≥1 of saturated triangular subsets and the filtration = (Gi)i≥0 induced by and M, is of Cousin type for M with respect to (Corollary (3.5)(3)).