On Formal Local Cohomology and Connectedness
نویسنده
چکیده
Let a denote an ideal of a local ring (R, m). Let M be a finitely generated Rmodule. There is a systematic study of the formal cohomology modules lim ←− H m(M/a M), i ∈ Z. We analyze their R-module structure, the upper and lower vanishing and non-vanishing in terms of intrinsic data of M, and its functorial behavior. These cohomology modules occur in relation to the formal completion of the punctured spectrum Spec R \ V (m). As a new cohomological data there is a description on the formal grade fgrade(a, M) defined as the minimal non-vanishing of the formal cohomology modules. There are various exact sequences concerning the formal cohomology modules. Among them a Mayer-Vietoris sequence for two ideals. It applies to new connectedness results. There are also relations to local cohomological dimensions.
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