Theorems · Theorem · algebraic geometry
AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_of_isNilpotent
∀ (X : AlgebraicGeometry.LocallyRingedSpace) (U : TopologicalSpace.Opens ↑↑X.toPresheafedSpace) (f : ↑(X.presheaf.obj (Opposite.op U))), IsNilpotent f → X.toRingedSpace.basicOpen f = ⊥
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Oppositestatement · cited by 8,081
- Bot.botstatement and proof · cited by 4,720
- TopCat.carrierstatement and proof · cited by 3,184
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- 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.PresheafedSpace.presheafstatement and proof · cited by 1,104
- CommRingCat.carrierstatement and proof · cited by 1,096
- pow_zeroproof · cited by 1,094
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot_of_isCompactproof · cited by 2