Threeadic.lean`

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1 declarations, 1 contain sorry, 0 declared as axioms

3-adic hardly ramified representations

Three-adic input results for the analysis of hardly ramified families: properties of R-linear representations on a finite ℤ_[3]-module which are hardly ramified at 3.

Imports (1)

FLT.GaloisRepresentation.HardlyRamified.Defs

Imported by 1 file

FLT.lean

theorem GaloisRepresentation.IsHardlyRamified.three_adic A 3-adic hardly ramified representation has trace(Frob_p) = 1 + p for all p ≠ 2,3 sorry line 31 source
Source documentation
A 3-adic hardly ramified representation has trace(Frob_p) = 1 + p for all p ≠ 2,3

depends on sorry what this means
Statement uses: CommRing, Algebra, PadicInt, OfNat.ofNat, Nat, Module.Finite, Module.Free, TopologicalSpace, IsTopologicalRing, IsLocalRing, IsModuleTopology, AddCommGroup, Module, Eq, Cardinal, Module.rank, GaloisRep, Rat, GaloisRepresentation.IsHardlyRamified, Odd and 13 more
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
110 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem three_adic {R : Type*} [CommRing R] [Algebra ℤ_[3] R] [Module.Finite ℤ_[3] R]
    [Module.Free ℤ_[3] R] [TopologicalSpace R] [IsTopologicalRing R] [IsLocalRing R]
    [IsModuleTopology ℤ_[3] R]
    (V : Type*) [AddCommGroup V] [Module R V] [Module.Finite R V] [Module.Free R V]
    (hV : Module.rank R V = 2) {ρ : GaloisRep ℚ R V}
    (hρ : IsHardlyRamified (show Odd 3 by decide) hV ρ) :
    ∀ p (hp : Nat.Prime p) (hp5 : 5 ≤ p),
      letI v := hp.toHeightOneSpectrumRingOfIntegersRat -- p as a finite place of ℚ
…
```
Mentions: GaloisRep, GaloisRepresentation.IsHardlyRamified