An extension of the Hartshorne theorem on the characterization of cofinite complexes (Researches on theory of isometries and preserver problems from a various point of view)

Abstract

This report is the announcement of the result on the characterization of cofinite complexes (the first one is in the talk at the RIMS conferencet). Let A be a homomorphic image of a Gorenstein ring of finite Krull dimension, J an ideal of A, and N^{cdot} a bounded-below complex of A-modules. Suppose that A is complete with respect to a J-adic topology. In this report, we introduce that N^{cdot} is a J-cofinite complex if and only if the support of H^{i}(N^{cdot}) is in V(J) for all i, and Ext^{j}(A/J, N^{cdot}) is of finite type for all j.