Theorems · Theorem · number theory
WeierstrassCurve.hasGoodReduction_iff_isElliptic_reduction
∀ (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- Cited by
- 1 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- IsUnitproof · cited by 1,602
- IsFractionRingstatement and proof · cited by 738
- WeierstrassCurvestatement and proof · cited by 394
- IsLocalRing.maximalIdealproof · cited by 297
- not_iff_notproof · cited by 159
- IsDedekindDomain.HeightOneSpectrum.asIdealproof · cited by 156
Cited by1
Results whose statement or proof uses this declaration.
- WeierstrassCurve.isGoodReduction_iff_isElliptic_reductionproof · cited by 0