Theorems · Theorem · algebraic geometry
AlgebraicGeometry.functionField_isFractionRing_of_isAffineOpen
∀ (X : AlgebraicGeometry.Scheme) [inst : AlgebraicGeometry.IsIntegral X] (U : X.Opens),
AlgebraicGeometry.IsAffineOpen U →
∀ [inst_1 : Nonempty ↥↑U], IsFractionRing ↑(X.presheaf.obj (Opposite.op U)) ↑X.functionField- Defined in
- Mathlib.AlgebraicGeometry.FunctionField
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites41
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Algebraproof · cited by 11,388
- CommSemiringproof · cited by 10,911
- SetLike.coeproof · cited by 8,199
- Oppositestatement · cited by 8,081
- TopCat.carrierstatement and proof · cited by 3,184
- Submonoidproof · cited by 3,086
- Set.Nonemptyproof · cited by 2,627
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
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