Theorems · Definition · algebraic geometry

WeierstrassCurve.Affine.pointEquiv

{R : Type r} →
  [inst : CommRing R] →
    (W' : WeierstrassCurve.Affine R) →
      [Nontrivial R] → [WeierstrassCurve.IsElliptic W'] → W'.Point ≃ WithZero { xy // W'.Equation xy.1 xy.2 }

The equivalence between the rational points on an elliptic curve E and the set of pairs ⟨x, y⟩ satisfying E.Equation x y with zero.

Defined in

Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point

Cited by

4 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingNontrivialWeierstrassCurve.IsElliptic