p_adic_langlands_conjecture
Provedalgebraalgebraic-geometry
p-adic Langlands program: For GL₂(ℚₚ), there is a correspondence between p-adic representations of Gal(ℚ̄ₚ/ℚₚ) and p-adic Banach space representations of GL₂(ℚₚ). Proved for GL₂ (Breuil-Mézard, Colmez, Kisin); general GLₙ and other groups open.
Preamble
import Mathlib
Formal statement
import Mathlib
theorem p_adic_langlands_conjecture (p : ℕ) (hp : Nat.Prime p) (n : ℕ) (hn : 1 ≤ n) :
∀ (rho : (ZMod p → ZMod p) → Matrix (Fin n) (Fin n) (ZMod p)),
∃ (pi : Matrix (Fin n) (Fin n) (ZMod p) → ℤ),
True := by
sorrySource