Theorems · Definition · number theory

WeierstrassCurve.IsMinimal.recOn

{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.IsMinimal R W → Sort u} →
                    (t : WeierstrassCurve.IsMinimal R W) →
                      ((val_Δ_maximal :
                            MaximalFor (fun C => WeierstrassCurve.IsIntegral R (C • W))
                              (fun C => WeierstrassCurve.valuation_Δ_aux R (C • W)) 1) →
                          motive ⋯) →
                        motive t

Defined in

Mathlib.AlgebraicGeometry.EllipticCurve.Reduction

Cited by

0 results in Mathlib

Foundations

Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainIsDiscreteValuationRingFieldAlgebraIsFractionRing