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单词 CoherentSheaf
释义

coherent sheaf


Let R be a ring with unity, and X=SpecR be its prime spectrum. Given an R-module M, one can define a presheafPlanetmathPlanetmathPlanetmath on X by defining its sectionsPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath on an open set U to be 𝒪X(U)RM. We call the sheafificationPlanetmathPlanetmath of this M~, and a sheaf of this form on X is called quasi-coherent. If M is a finitely generated module, then M~ is called coherent. A sheaf on an arbitrary scheme X is called (quasi-)coherent if it is (quasi-)coherent on each open affine subset of X.

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更新时间:2025/5/4 6:14:17