AlgebraicCurve.DivisorialWeilPairingData.perfect_of_divisible_coprime_of_isAlgClosed
Source context 10 commands
Surrounding namespaces, section variables, and local commands at this declaration.
section ProofImplementation
namespace JacobianVarieties.WeilPairing.Proofs.ClosedFieldPerfectPairing
attribute [-instance]
AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
AlgebraicCurve.Pic0.instModuleZModTorsion
AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
AlgebraicCurve.SemilinearAut.instSMulTorsion
AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
AlgebraicCurve.Place.instIsPrimeCenter
AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
AlgebraicCurve.IsCurveOver.instNontrivialKaehler
AlgebraicCurve.IsCurveOver.instFreeKaehler
AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
AlgebraicCurve.IsCurveOver.instFiniteResidue
AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
attribute [-simp]
AlgebraicCurve.Divisor.mapRestrict_single
AlgebraicCurve.Divisor.pushforward_single
AlgebraicCurve.Place.coe_restrictInclusion
AlgebraicCurve.Place.mem_fiber
AlgebraicCurve.Place.restrict_toValuationSubring
AlgebraicCurve.Divisor.degree_pushforward
AlgebraicCurve.Place.restrictResidueMap_residue
AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
AlgebraicCurve.SemilinearAut.toRingAut_inv
AlgebraicCurve.SemilinearAut.smul_def
AlgebraicCurve.SemilinearAut.smul_single
AlgebraicCurve.SemilinearAut.smul_toValuationSubring
AlgebraicCurve.SemilinearAut.baseAut_inv
AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
AlgebraicCurve.SemilinearAut.toRingAut_one
AlgebraicCurve.SemilinearAut.deg_smul
AlgebraicCurve.SemilinearAut.degree_smul
AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
AlgebraicCurve.SemilinearAut.baseAut_mul
AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
AlgebraicCurve.SemilinearAut.baseAut_one
AlgebraicCurve.SemilinearAut.ofAlgAut_smul
AlgebraicCurve.SemilinearAut.coe_torsion_smul
AlgebraicCurve.SemilinearAut.toRingAut_mul
AlgebraicCurve.Place.placeOfPrime_toValuationSubring
AlgebraicCurve.Place.mem_fiberOver
AlgebraicCurve.Place.fiberEquiv_symm_apply
AlgebraicCurve.Place.fiberEquiv_apply
AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
AlgebraicCurve.Place.congrEquiv_symm_apply
AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
AlgebraicCurve.Place.congrEquiv_apply
AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
attribute [-simp]
AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
RatFunc.denom_X_pow
RatFunc.powerBasisAdjoinXPow_dim
RatFunc.powerBasisAdjoinXPow_gen
RatFunc.intDegree_X_pow
RatFunc.num_X_pow
open AlgebraicCurve
with_weak_namespace _root_.AlgebraicCurve.DivisorialWeilPairingDataLean source · statement
theorem perfect_of_divisible_coprime_of_isAlgClosed.{u, v}
{K : Type u} {F : Type v} [Field K] [Field F] [Algebra K F] [IsAlgClosed K]
[Algebra (RatFunc K) F] [IsScalarTower K (RatFunc K) F] [FiniteDimensional (RatFunc K) F]
[HasPrincipalDivisors K F] {n : ℕ} [NeZero n] (hn : (n : K) ≠ 0)
(hdiv : ∀ (L' : Type v) [Field L'] [Algebra K L'] [Algebra (RatFunc K) L']
[IsScalarTower K (RatFunc K) L'] [FiniteDimensional (RatFunc K) L'],
∀ (m : ℤ), (m : K) ≠ 0 → ∀ x : Pic0 K L', ∃ y, m • y = x)
[Finite (Pic0.torsion K F n)]
(e : DivisorialWeilPairingData K F n) : e.Perfect