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← GaloisRepresentation.IsHardlyRamified.three_adic
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Lean 4.29.1
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Mathlib v4.29.1
Ubuntu 24.04 LTS · x86_64 · toolchain via elan
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13 days ago
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Lean 4 / Mathlib
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import Mathlib /-- A 3-adic hardly ramified representation has trace(Frob_p) = 1 + p for all p ≠ 2,3 -/ 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 (ρ.toLocal v (Frob v)).trace _ _ = 1 + p := sorry
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