Theorems · Definition · number theory

WeierstrassCurve.HasAdditiveReduction.casesOn

{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} →
                  {motive : WeierstrassCurve.HasAdditiveReduction R W → Sort u} →
                    (t : WeierstrassCurve.HasAdditiveReduction R W) →
                      ([toIsMinimal : WeierstrassCurve.IsMinimal R W] →
                          (badReduction :
                              (IsDedekindDomain.HeightOneSpectrum.valuation K (IsDiscreteValuationRing.maximalIdeal R))
                                  W.Δ <
                                1) →
                            (additiveReduction :
                                (IsDedekindDomain.HeightOneSpectrum.valuation K
                                      (IsDiscreteValuationRing.maximalIdeal R))
                                    W.c₄ <
                                  1) →
                              motive ⋯) →
                        motive t

Defined in

Mathlib.AlgebraicGeometry.EllipticCurve.Reduction

Cited by

1 results in Mathlib

Foundations

Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainIsDiscreteValuationRingFieldAlgebraIsFractionRing