Theorems · Definition · algebraic geometry
AlgebraicGeometry.AffineSpace.SpecIso
(n : Type u) →
(R : CommRingCat) →
AlgebraicGeometry.AffineSpace n (AlgebraicGeometry.Spec R) ≅
AlgebraicGeometry.Spec (CommRingCat.of (MvPolynomial n ↑R))The affine space over an affine base is isomorphic to the spectrum of the polynomial ring.
- Defined in
- Mathlib.AlgebraicGeometry.AffineSpace
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsuppstatement · cited by 5,255
- CategoryTheory.Isostatement · cited by 3,963
- AlgebraicGeometry.Schemestatement · cited by 2,540
- CommRingCatstatement and proof · cited by 2,333
- MvPolynomialstatement · cited by 2,140
- CommRingCat.carrierstatement · cited by 1,096
- CategoryTheory.Iso.symmproof · cited by 993
- AlgebraicGeometry.Specstatement and proof · cited by 626
- CategoryTheory.Iso.transproof · cited by 566
- CategoryTheory.Functor.mapIsoproof · cited by 224
- AlgebraicGeometry.Scheme.ΓSpecIsoproof · cited by 106
- AlgebraicGeometry.Scheme.Specproof · cited by 57
Cited by8
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.AffineSpace.SpecIso_inv_overstatement · cited by 4
- AlgebraicGeometry.AffineSpace.SpecIso_inv_appTop_coordstatement · cited by 1
- AlgebraicGeometry.AffineSpace.SpecIso_inv_over_assocstatement and proof · cited by 1
- AlgebraicGeometry.AffineSpace.SpecIso_hom_appTopstatement · cited by 0
- AlgebraicGeometry.AffineSpace.isOpenMap_overproof · cited by 0
- AlgebraicGeometry.AffineSpace.isIntegralHom_over_iff_isEmptyproof · cited by 0
- AlgebraicGeometry.AffineSpace.mapSpecMapproof · cited by 0
- AlgebraicGeometry.AffineSpace.map_SpecMapstatement and proof · cited by 0