Theorems · Definition · algebraic geometry

WeierstrassCurve.Affine.nonsingularPointEquivSubtype

{R : Type r} →
  [inst : CommRing R] →
    {W' : WeierstrassCurve.Affine R} →
      {p : W'.Point → Prop} →
        p WeierstrassCurve.Affine.Point.zero →
          { P // p P } ≃
            WithZero { xy // ∃ (h : W'.Nonsingular xy.1 xy.2), p (WeierstrassCurve.Affine.Point.some xy.1 xy.2 h) }

The equivalence between the nonsingular points on a Weierstrass curve W in affine coordinates satisfying a predicate and the set of pairs ⟨x, y⟩ satisfying W.Nonsingular x y with zero.

Defined in

Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point

Cited by

4 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRing