Theorems · Theorem · algebraic geometry
AlgebraicGeometry.essImage_hopfSpec
∀ {R : CommRingCat} {G : CategoryTheory.Grp (CategoryTheory.Over (AlgebraicGeometry.Spec R))},
(AlgebraicGeometry.hopfSpec R).essImage G ↔ AlgebraicGeometry.IsAffine G.X.leftThe essential image of R-Hopf algebras under Spec is precisely affine group schemes over
Spec R.
- Defined in
- Mathlib.AlgebraicGeometry.Group.Affine
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Oppositestatement · cited by 8,081
- AlgebraicGeometry.Schemestatement · cited by 2,540
- CommRingCatstatement and proof · cited by 2,333
- CommRingCat.carrierstatement · cited by 1,096
- CategoryTheory.Overstatement and proof · cited by 935
- AlgebraicGeometry.Specstatement and proof · cited by 626
- CategoryTheory.Over.leftstatement and proof · cited by 541
- AlgebraicGeometry.IsAffinestatement and proof · cited by 159
- CategoryTheory.Grpstatement and proof · cited by 144
- CategoryTheory.Grp.Xstatement and proof · cited by 99
- CategoryTheory.Functor.essImagestatement · cited by 82
- CommHopfAlgCatstatement · cited by 38
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