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)

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  • An extension of the Hartshorne theorem on the characterization of cofinite complexes

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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.

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  • RIMS Kokyuroku

    RIMS Kokyuroku 2118 33-37, 2019-07

    京都大学数理解析研究所

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