Theorems · Theorem · number theory

WeierstrassCurve.isGoodReduction_iff_isElliptic_reduction

Deprecated since 2026-03-04Use WeierstrassCurve.hasGoodReduction_iff_isElliptic_reduction instead.

∀ (R : Type u_1) [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDiscreteValuationRing R] {K : Type u_2}
  [inst_3 : Field K] [inst_4 : Algebra R K] [inst_5 : IsFractionRing R K] {W : WeierstrassCurve K}
  [hW : WeierstrassCurve.IsMinimal R W],
  WeierstrassCurve.HasGoodReduction R W ↔ (WeierstrassCurve.reduction R W).IsElliptic

Alias of WeierstrassCurve.hasGoodReduction_iff_isElliptic_reduction.

Defined in

Mathlib.AlgebraicGeometry.EllipticCurve.Reduction

Cited by

0 results in Mathlib

Foundations

Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainIsDiscreteValuationRingFieldAlgebraIsFractionRingWeierstrassCurve.IsMinimal