ModThree.lean`

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1 declarations, 1 contain sorry, 0 declared as axioms

Mod-3 hardly ramified representations

A mod-3 hardly ramified representation is shown to be an extension of the trivial character by the mod-3 cyclotomic character.

Imports (1)

FLT.GaloisRepresentation.HardlyRamified.Defs

Imported by 1 file

FLT.lean

theorem GaloisRepresentation.IsHardlyRamified.mod_three A mod 3 hardly ramified representation is an extension of trivial by cyclo sorry line 27 source
Source documentation
A mod 3 hardly ramified representation is an extension of trivial by cyclo

depends on sorry what this means
Statement uses: Finite, Field, Algebra, PadicInt, OfNat.ofNat, Nat, TopologicalSpace, DiscreteTopology, AddCommGroup, Module, Module.Finite, Module.Free, Eq, Cardinal, Module.rank, GaloisRep, Rat, GaloisRepresentation.IsHardlyRamified, Odd, Exists and 5 more
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
64 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
```
theorem mod_three {k : Type u} [Finite k] [Field k] [Algebra ℤ_[3] k] --
    [TopologicalSpace k] [DiscreteTopology k]
    (V : Type*) [AddCommGroup V] [Module k V] [Module.Finite k V] [Module.Free k V]
    (hV : Module.rank k V = 2) {ρ : GaloisRep ℚ k V}
    (hρ : IsHardlyRamified (show Odd 3 by decide) hV ρ) :
    ∃ (π : V →ₗ[k] k) (_ : Function.Surjective π),
    ∀ g : Γ ℚ, ∀ v : V, π (ρ g v) = π v := by
…
```
Mentions: GaloisRep, GaloisRepresentation.IsHardlyRamified