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Theorems · Definition · algebraic geometry

WeierstrassCurve.Affine.CoordinateRing

{R : Type r} → [CommRing R] → WeierstrassCurve.Affine R → Type r

The affine coordinate ring R[W] := R[X, Y] / ⟨W(X, Y)⟩ of a Weierstrass curve W.

Defined in
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point
Cited by
39 results in Mathlib
Foundations
Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

WeierstrassCurve.Affine.CoordinateRing.mk · cited by 25CoordinateRing.mkWeierstrassCurve.Affine.CoordinateRing.XYIdeal · cited by 9CoordinateRing.XYIdealWeierstrassCurve.Affine.CoordinateRing.basis · cited by 8CoordinateRing.basisWeierstrassCurve.Affine.CoordinateRing.XYIdeal' · cited by 7CoordinateRing.XYIdeal'WeierstrassCurve.Affine.FunctionField · cited by 6Affine.FunctionFieldWeierstrassCurve.Affine.Point.toClass · cited by 5Point.toClassWeierstrassCurve.Affine.CoordinateRing.XClass · cited by 5CoordinateRing.XClassWeierstrassCurve.Affine.CoordinateRing.basis_one · cited by 4CoordinateRing.basis_oneWeierstrassCurve.Affine.CoordinateRing.basis_zero · cited by 4CoordinateRing.basis_zeroWeierstrassCurve.Affine.CoordinateRing.XIdeal · cited by 3CoordinateRing.XIdealWeierstrassCurve.Affine.CoordinateRing.YClass · cited by 3CoordinateRing.YClassWeierstrassCurve.Affine.CoordinateRing.map · cited by 3CoordinateRing.mapWeierstrassCurve.Affine.CoordinateRing.smul · cited by 3CoordinateRing.smulWeierstrassCurve.Affine.CoordinateRing.XClass_ne_zero · cited by 2CoordinateRing.XClass_ne_…WeierstrassCurve.Affine.CoordinateRing.basis_apply · cited by 2CoordinateRing.basis_applyCommRing · cited by 17173CommRingAdjoinRoot · cited by 177AdjoinRootWeierstrassCurve.Affine · cited by 174WeierstrassCurve.AffineWeierstrassCurve.Affine.polynomial · cited by 61Affine.polynomialAffine.CoordinateRingCITED BYCITES

Cites4

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Cited by51

Results whose statement or proof uses this declaration.