Theorems · Theorem · algebraic geometry
AlgebraicGeometry.exists_eq_pow_mul_of_isAffineOpen
∀ (X : AlgebraicGeometry.Scheme) (U : X.Opens),
AlgebraicGeometry.IsAffineOpen U →
∀ (f : ↑(X.presheaf.obj (Opposite.op U))) (x : ↑(X.presheaf.obj (Opposite.op (X.basicOpen f)))),
∃ n y, TopCat.Presheaf.restrictOpen y (X.basicOpen f) ⋯ = TopCat.Presheaf.restrictOpen f (X.basicOpen f) ⋯ ^ n * x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- RingHomstatement · cited by 10,189
- Oppositestatement · cited by 8,081
- Algebra.algebraMapproof · cited by 4,706
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- mul_commproof · cited by 2,262
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.exists_eq_pow_mul_of_isCompact_of_isQuasiSeparatedproof · cited by 1