Theorems · Definition · algebraic geometry

WeierstrassCurve.Jacobian.negMap

{R : Type r} →
  [inst : CommRing R] →
    WeierstrassCurve.Jacobian R → WeierstrassCurve.Jacobian.PointClass R → WeierstrassCurve.Jacobian.PointClass R

The negation of a Jacobian point class on a Weierstrass curve W. If P is a Jacobian point representative on W, then W.negMap ⟦P⟧ is definitionally equivalent to W.neg P.

Defined in: Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point
Cited by: 5 results in Mathlib
Foundations: Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing

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Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CommRingstatement and proof · cited by 17,173
WeierstrassCurve.Jacobianstatement and proof · cited by 232
WeierstrassCurve.Jacobian.PointClassstatement and proof · cited by 21
WeierstrassCurve.Jacobian.negproof · cited by 19
Quotient.mapproof · cited by 7
WeierstrassCurve.Jacobian.neg_equivproof · cited by 0

Cited by5

Results whose statement or proof uses this declaration.

WeierstrassCurve.Jacobian.negMap_eqstatement · cited by 2
WeierstrassCurve.Jacobian.Point.neg_pointstatement · cited by 0
WeierstrassCurve.Jacobian.negMap_of_Z_eq_zerostatement · cited by 0
WeierstrassCurve.Jacobian.negMap_of_Z_ne_zerostatement · cited by 0
WeierstrassCurve.Jacobian.nonsingularLift_negMapstatement · cited by 0