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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.germToFunctionField

(X : AlgebraicGeometry.Scheme) →
  [inst : IrreducibleSpace ↥X] → (U : X.Opens) → [h : Nonempty ↥↑U] → X.presheaf.obj (Opposite.op U) ⟶ X.functionField

The restriction map from a component to the function field.

Defined in
Mathlib.AlgebraicGeometry.FunctionField
Cited by
7 results in Mathlib
Foundations
Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
IrreducibleSpaceNonempty
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.Scheme.algebraMap_germ_eq_germToFunctionField · cited by 1Scheme.algebraMap_germ_eq…AlgebraicGeometry.Scheme.ordHom_of_isUnit · cited by 1Scheme.ordHom_of_isUnitAlgebraicGeometry.Scheme.germToFunctionField.congr_simp · cited by 0germToFunctionField.congr…AlgebraicGeometry.Scheme.ord_le_smul · cited by 0Scheme.ord_le_smulAlgebraicGeometry.Scheme.ord_of_isUnit · cited by 0Scheme.ord_of_isUnitAlgebraicGeometry.exists_isUnit_germ_eq · cited by 0AlgebraicGeometry.exists_…AlgebraicGeometry.Scheme.germToFunctionField_injective · cited by 0Scheme.germToFunctionFiel…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objOpposite · cited by 8081OppositeTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…AlgebraicGeometry.Scheme.Opens · cited by 1149Scheme.OpensAlgebraicGeometry.PresheafedSpace.presheaf · cited by 1104PresheafedSpace.presheafAlgebraicGeometry.Scheme.Opens.toScheme · cited by 433Opens.toSchemeTopCat.Presheaf.germ · cited by 208Presheaf.germScheme.germToFunctionFieldCITED BYCITES

Cites18

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by7

Results whose statement or proof uses this declaration.