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Theorems · Definition · number theory

WeierstrassCurve.integralModel

(R : Type u_1) →
  [inst : CommRing R] →
    {K : Type u_2} →
      [inst_1 : Field K] →
        [inst_2 : Algebra R K] → (W : WeierstrassCurve K) → [hW : WeierstrassCurve.IsIntegral R W] → WeierstrassCurve R

An integral model of an integral Weierstrass curve.

Defined in
Mathlib.AlgebraicGeometry.EllipticCurve.Reduction
Cited by
18 results in Mathlib
Foundations
Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingFieldAlgebraWeierstrassCurve.IsIntegral

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

WeierstrassCurve.baseChange_integralModel_eq · cited by 12WeierstrassCurve.baseChan…WeierstrassCurve.integralModel_Δ_eq · cited by 2WeierstrassCurve.integral…WeierstrassCurve.reduction · cited by 2WeierstrassCurve.reductionWeierstrassCurve.integralModel_c₄_eq · cited by 1WeierstrassCurve.integral…WeierstrassCurve.HasSplitMultiplicativeReduction.casesOn · cited by 1HasSplitMultiplicativeRed…WeierstrassCurve.hasGoodReduction_iff_isElliptic_reduction · cited by 1WeierstrassCurve.hasGoodR…WeierstrassCurve.integralModel_a₁_eq · cited by 0WeierstrassCurve.integral…WeierstrassCurve.integralModel_a₂_eq · cited by 0WeierstrassCurve.integral…WeierstrassCurve.integralModel_a₃_eq · cited by 0WeierstrassCurve.integral…WeierstrassCurve.integralModel_a₄_eq · cited by 0WeierstrassCurve.integral…WeierstrassCurve.integralModel_a₆_eq · cited by 0WeierstrassCurve.integral…WeierstrassCurve.integralModel_b₂_eq · cited by 0WeierstrassCurve.integral…WeierstrassCurve.integralModel_b₄_eq · cited by 0WeierstrassCurve.integral…WeierstrassCurve.integralModel_b₆_eq · cited by 0WeierstrassCurve.integral…WeierstrassCurve.integralModel_b₈_eq · cited by 0WeierstrassCurve.integral…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraField · cited by 7404FieldWeierstrassCurve · cited by 394WeierstrassCurveWeierstrassCurve.IsIntegral · cited by 23WeierstrassCurve.IsIntegr…WeierstrassCurve.IsIntegral.integral · cited by 2IsIntegral.integralWeierstrassCurve.integralModelCITED BYCITES

Cites6

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Cited by21

Results whose statement or proof uses this declaration.