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- Sheaf_spanned_by_global_sections abstract "In mathematics, a sheaf spanned by global sections is a sheaf F on a locally ringed space X, with structure sheaf OX that is of a rather simple type. Assume F is a sheaf of abelian groups. Then it is asserted that if A is the abelian group of global sections, i.e.A = Γ(F,X)then for any open set U of X, ρ(A) spans F(U) as an OU-module. Here ρ = ρX,Uis the restriction map. In words, all sections of F are locally generated by the global sections.An example of such a sheaf is that associated in algebraic geometry to an R-module M, R being any commutative ring, on the spectrum of a ring Spec(R).Another example: according to Cartan's theorem A, any coherent sheaf on a Stein manifold is spanned by global sections.".
- Sheaf_spanned_by_global_sections wikiPageID "1054325".
- Sheaf_spanned_by_global_sections wikiPageRevisionID "535078041".
- Sheaf_spanned_by_global_sections hasPhotoCollection Sheaf_spanned_by_global_sections.
- Sheaf_spanned_by_global_sections subject Category:Sheaf_theory.
- Sheaf_spanned_by_global_sections subject Category:Topological_methods_of_algebraic_geometry.
- Sheaf_spanned_by_global_sections type Ability105616246.
- Sheaf_spanned_by_global_sections type Abstraction100002137.
- Sheaf_spanned_by_global_sections type Cognition100023271.
- Sheaf_spanned_by_global_sections type Know-how105616786.
- Sheaf_spanned_by_global_sections type Method105660268.
- Sheaf_spanned_by_global_sections type PsychologicalFeature100023100.
- Sheaf_spanned_by_global_sections type TopologicalMethodsOfAlgebraicGeometry.
- Sheaf_spanned_by_global_sections comment "In mathematics, a sheaf spanned by global sections is a sheaf F on a locally ringed space X, with structure sheaf OX that is of a rather simple type. Assume F is a sheaf of abelian groups. Then it is asserted that if A is the abelian group of global sections, i.e.A = Γ(F,X)then for any open set U of X, ρ(A) spans F(U) as an OU-module. Here ρ = ρX,Uis the restriction map.".
- Sheaf_spanned_by_global_sections label "Sheaf spanned by global sections".
- Sheaf_spanned_by_global_sections sameAs m.041_k4.
- Sheaf_spanned_by_global_sections sameAs Q7492161.
- Sheaf_spanned_by_global_sections sameAs Q7492161.
- Sheaf_spanned_by_global_sections sameAs Sheaf_spanned_by_global_sections.
- Sheaf_spanned_by_global_sections wasDerivedFrom Sheaf_spanned_by_global_sections?oldid=535078041.
- Sheaf_spanned_by_global_sections isPrimaryTopicOf Sheaf_spanned_by_global_sections.