Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot_of_isCompact
∀ {X : AlgebraicGeometry.Scheme} {U : X.Opens},
IsCompact ↑U → ∀ (f : ↑(X.presheaf.obj (Opposite.op U))), IsNilpotent f ↔ X.basicOpen f = ⊥A section over a compact open of a scheme is nilpotent if and only if its associated basic open is empty.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
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
- CategoryTheory.Functor.mapproof · cited by 8,698
- SetLike.coestatement and proof · cited by 8,199
- Oppositestatement · cited by 8,081
- Bot.botstatement and proof · cited by 4,720
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- mul_oneproof · cited by 3,885
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- le_reflproof · cited by 2,061
- TopologicalSpace.Opensstatement · cited by 2,040
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_botproof · cited by 0