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- Base_change abstract "In mathematics, especially in algebraic geometry, base change refers to a number of similar theorems concerning the cohomology of sheaves on algebro-geometric objects such as varieties or schemes. The situation of a base change theorem typically is as follows: given two maps of, say, schemes, , , let and be the projections from the fiber product to and , respectively. Moreover, let a sheaf on X' be given. Then, there is a natural map (obtained by means of adjunction)Depending on the type of sheaf, and on the type of the morphisms g and f, this map is an isomorphism (of sheaves on Y) in some cases. Here denotes the higher direct image of under g. As the stalk of this sheaf at a point on Y is closely related to the cohomology of the fiber of the point under g, this statement is paraphrased by saying that "cohomology commutes with base extension".".
- Base_change wikiPageID "1816827".
- Base_change wikiPageRevisionID "504983874".
- Base_change hasPhotoCollection Base_change.
- Base_change subject Category:Sheaf_theory.
- Base_change comment "In mathematics, especially in algebraic geometry, base change refers to a number of similar theorems concerning the cohomology of sheaves on algebro-geometric objects such as varieties or schemes. The situation of a base change theorem typically is as follows: given two maps of, say, schemes, , , let and be the projections from the fiber product to and , respectively. Moreover, let a sheaf on X' be given.".
- Base_change label "Base change".
- Base_change sameAs m.0k8vz6r.
- Base_change sameAs Q4866384.
- Base_change sameAs Q4866384.
- Base_change wasDerivedFrom Base_change?oldid=504983874.
- Base_change isPrimaryTopicOf Base_change.