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Theorems · Theorem · algebraic geometry

WeierstrassCurve.Projective.map_nonsingular

∀ {R : Type r} [inst : CommRing R] (W' : WeierstrassCurve.Projective R) {S : Type s} [inst_1 : CommRing S]
  {f : R →+* S}, Function.Injective ⇑f → ∀ (P : Fin 3 → R), (W'.map f).Nonsingular (⇑f ∘ P) ↔ W'.Nonsingular P
Defined in
Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basic
Cited by
1 results in Mathlib
Foundations
Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRing
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WeierstrassCurve.Projective.baseChange_nonsingular · cited by 0Projective.baseChange_non…DFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingRingHom · cited by 10189RingHomWeierstrassCurve.Projective · cited by 244WeierstrassCurve.Projecti…MvPolynomial.eval · cited by 157MvPolynomial.evalWeierstrassCurve.Projective.Equation · cited by 88Projective.EquationWeierstrassCurve.Projective.Nonsingular · cited by 37Projective.NonsingularWeierstrassCurve.Projective.map · cited by 25Projective.mapmap_ne_zero_iff · cited by 24map_ne_zero_iffWeierstrassCurve.Projective.polynomialX · cited by 19Projective.polynomialXWeierstrassCurve.Projective.polynomialY · cited by 10Projective.polynomialYMvPolynomial.eval_map · cited by 9MvPolynomial.eval_mapWeierstrassCurve.Projective.polynomialZ · cited by 7Projective.polynomialZWeierstrassCurve.Projective.map_equation · cited by 2Projective.map_equationWeierstrassCurve.Projective.map_polynomialY · cited by 2Projective.map_polynomialYProjective.map_nonsingularCITED BYCITES

Cites17

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Cited by1

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