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riccardobrasca committed Feb 13, 2025
1 parent 7d7ef20 commit c2bbb3b
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14 changes: 7 additions & 7 deletions FltRegular/NumberTheory/Unramified.lean
Original file line number Diff line number Diff line change
Expand Up @@ -20,7 +20,7 @@ import Mathlib.NumberTheory.RamificationInertia.Basic
is separable for some ideal `p` of `R` (with `f` being the minpoly of `α` over `R`), then `S/R` is
unramified at `p`.
-/
open BigOperators UniqueFactorizationMonoid
open BigOperators UniqueFactorizationMonoid Ideal

attribute [local instance] FractionRing.liftAlgebra

Expand Down Expand Up @@ -150,8 +150,8 @@ lemma isUnramifiedAt_of_Separable_minpoly' [Algebra.IsSeparable K L]
have := IsIntegralClosure.isFractionRing_of_finite_extension R K L S
have := aeval_derivative_mem_differentIdeal R K L x hx'
have H : RingHom.comp (algebraMap (FractionRing R) (FractionRing S))
(FractionRing.algEquiv R K).symm.toRingEquiv =
RingHom.comp (FractionRing.algEquiv S L).symm.toRingEquiv (algebraMap K L) := by
(FractionRing.algEquiv R K).symm.toRingEquiv =
RingHom.comp (FractionRing.algEquiv S L).symm.toRingEquiv (algebraMap K L) := by
apply IsLocalization.ringHom_ext R⁰
ext
simp only [AlgEquiv.toRingEquiv_eq_coe, RingHom.coe_comp, RingHom.coe_coe,
Expand All @@ -177,12 +177,12 @@ lemma isUnramifiedAt_of_Separable_minpoly' [Algebra.IsSeparable K L]
have := hP.2.1
rw [Ideal.under_def] at this
have := (separable_map (Ideal.quotientMap P (algebraMap R S) this.symm.ge)).mpr h
rw [map_map, Ideal.quotientMap_comp_mk] at this
rw [Polynomial.map_map, Ideal.quotientMap_comp_mk] at this
obtain ⟨a, b, e⟩ := this
apply_fun (aeval (Ideal.Quotient.mk P x)) at e
simp_rw [← Ideal.Quotient.algebraMap_eq, ← map_map, derivative_map, map_add, map_mul,
aeval_map_algebraMap, aeval_algebraMap_apply, minpoly.aeval, hxP, map_zero, mul_zero,
zero_add, map_one, zero_ne_one] at e
simp_rw [← Ideal.Quotient.algebraMap_eq, ← Polynomial.map_map, derivative_map, map_add,
_root_.map_mul, aeval_map_algebraMap, aeval_algebraMap_apply, minpoly.aeval, hxP, map_zero,
mul_zero, zero_add, map_one, zero_ne_one] at e
· rwa [Ideal.IsDedekindDomain.ramificationIdx_eq_factors_count _
(isMaximal_of_mem_primesOver hpbot hP).isPrime (ne_bot_of_mem_primesOver hpbot hP),
Multiset.one_le_count_iff_mem, ← Multiset.mem_toFinset, ← primesOverFinset,
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14 changes: 7 additions & 7 deletions lake-manifest.json
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Expand Up @@ -5,7 +5,7 @@
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Expand All @@ -25,7 +25,7 @@
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Expand Down Expand Up @@ -85,7 +85,7 @@
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Expand All @@ -95,7 +95,7 @@
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Expand All @@ -105,10 +105,10 @@
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Expand All @@ -135,7 +135,7 @@
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