Theorems · Theorem · algebraic geometry
AlgebraicGeometry.genericPoint_eq_bot_of_affine
∀ (R : CommRingCat) [inst : IsDomain ↑R], genericPoint ↥(AlgebraicGeometry.Spec R) = ⊥
- Defined in
- Mathlib.AlgebraicGeometry.FunctionField
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsDomain
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- SetLike.coeproof · cited by 8,199
- Idealproof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- Set.univproof · cited by 3,945
- TopCat.carrierstatement and proof · cited by 3,184
- CommRingCatstatement and proof · cited by 2,333
- IsDomainstatement and proof · cited by 2,196
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.functionField_isFractionRing_of_isAffineOpenproof · cited by 0