FrobeniusRiou sorrys #137
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FrobeniusRiou sorrys #137
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…nto ImperialCollegeLondon-main
Imperial college london main
Merge Update
kbuzzard
reviewed
Oct 1, 2024
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| /-- | ||
| private theorem F_descent_monic | ||
| (hFull : ∀ (b : B), (∀ (g : G), g • b = b) → ∃ a : A, b = a) (b : B) : | ||
| ∃ M : A[X], (M : B[X]) = F G b ∧ Monic M := by | ||
| have : F G b ∈ Polynomial.lifts (algebraMap A B) := by | ||
| choose M hM using F_descent hFull b | ||
| use M; exact hM | ||
| choose M hM using lifts_and_degree_eq_and_monic this (F_monic b) | ||
| use M | ||
| exact ⟨hM.1, hM.2.2⟩ | ||
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| variable (G) in | ||
| noncomputable def M [Finite G] (b : B) : A[X] := (F_descent_monic hFull b).choose | ||
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| theorem M_spec (b : B) : ((M G hFull b : A[X]) : B[X]) = F G b := | ||
| (F_descent_monic hFull b).choose_spec.1 | ||
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| theorem M_spec' (b : B) : (map (algebraMap A B) (M G hFull b)) = F G b := | ||
| (F_descent_monic hFull b).choose_spec.1 | ||
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| theorem M_monic (b : B) : (M G hFull b).Monic := (F_descent_monic hFull b).choose_spec.2 | ||
| --/ |
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