Torsion.lean`

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1 declarations, 1 contain sorry, 0 declared as axioms

Torsion of an elliptic curve over a separably closed field

Let E be an elliptic curve over a separably closed field k and let n be a natural number which is nonzero in k. Then the n-torsion subgroup of E(k) is free of rank 2 over ℤ/nℤ.

Imports (3)

Imported by 1 file

FLT.lean

theorem WeierstrassCurve.torsion_rank_two then the n-torsion of E(k) is free rank 2 over ℤ/nℤ sorry line 36 source
Source comment
then the n-torsion of E(k) is free rank 2 over ℤ/nℤ

depends on sorry what this means
Statement uses: Field, IsSepClosed, DecidableEq, WeierstrassCurve, WeierstrassCurve.IsElliptic, Nat, NeZero, Nonempty, AddEquiv, Subtype, WeierstrassCurve.Affine.Point, WeierstrassCurve.Affine.baseChange, Membership.mem, AddSubgroup, AddSubgroup.torsionBy, Int, Prod, ZMod
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
49 instances, coercions and auxiliary constants left out.
```
theorem WeierstrassCurve.torsion_rank_two :
    Nonempty (AddSubgroup.torsionBy (E⁄k).Point (n : ℤ) ≃+ (ZMod n) × (ZMod n)) :=
…
```