Int Valuation comap
IsDedekindDomain.HeightOneSpectrum.intValuation_comap
Plain-language statement
If w | v then for a ∈ A we have w(a)=v(a)^e where e is the ramification index.
Exact Lean statement
lemma intValuation_comap (hAB : Function.Injective (algebraMap A B))
(w : HeightOneSpectrum B) (x : A) :
(under A w).intValuation x ^
(Ideal.ramificationIdx' (under A w).asIdeal w.asIdeal) =
w.intValuation (algebraMap A B x)Formal artifact
Lean source
lemma intValuation_comap (hAB : Function.Injective (algebraMap A B)) (w : HeightOneSpectrum B) (x : A) : (under A w).intValuation x ^ (Ideal.ramificationIdx' (under A w).asIdeal w.asIdeal) = w.intValuation (algebraMap A B x) := by classical have h_ne_zero := ramificationIdx_ne_zero A B hAB w by_cases hx : x = 0 · simpa [hx] simp only [intValuation, Valuation.coe_mk, MonoidWithZeroHom.coe_mk, ZeroHom.coe_mk] change (ite _ _ _) ^ _ = ite _ _ _ rw [map_eq_zero_iff _ hAB, if_neg hx, if_neg hx, ← Set.image_singleton, ← Ideal.map_span, mk_count_factors_map _ _ hAB, mul_comm, WithZero.exp, WithZero.exp] simp- Project
- Fermat's Last Theorem
- License
- Apache-2.0
- Commit
- 8dd808888295
- Source
- FLT/DedekindDomain/IntegralClosure.lean:96-109
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