Paper IX · Lean source

InvalidPrescribedParameter.lean

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polynomial_regularity/controls/InvalidPrescribedParameter.lean10 lines

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1 module
2 public import PolynomialParameterControls
3 @[expose] public section
4 open Komorebi.PolynomialParameterControls Komorebi.PolynomialPadicLift
5 
6 -- Full Jacobian surjectivity does not allow an arbitrary prescribed solved block.
7 -- X^2-T is smooth at the origin modulo two, but T=2 has no p-adic root.
8 example : ∃ a : Fin (1+1) → ℤ_[2],
9     padicEval 2 squareMinusParameter a = 0 ∧ a 1 = 2 := by
10   exact no_root_at_parameter_two

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Back to Paper IX: Arithmetic Packets, Dyadic Towers, and Local Polynomial Deformation