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riccardobrasca committed Oct 29, 2024
1 parent 33953c1 commit 63ba377
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2 changes: 0 additions & 2 deletions FltRegular.lean
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Expand Up @@ -6,7 +6,6 @@ import FltRegular.CaseII.Statement
import FltRegular.FLT5
import FltRegular.FltRegular
import FltRegular.MayAssume.Lemmas
import FltRegular.NumberTheory.AuxLemmas
import FltRegular.NumberTheory.Cyclotomic.CaseI
import FltRegular.NumberTheory.Cyclotomic.CyclRat
import FltRegular.NumberTheory.Cyclotomic.CyclotomicUnits
Expand All @@ -15,7 +14,6 @@ import FltRegular.NumberTheory.Cyclotomic.GaloisActionOnCyclo
import FltRegular.NumberTheory.Cyclotomic.MoreLemmas
import FltRegular.NumberTheory.Cyclotomic.UnitLemmas
import FltRegular.NumberTheory.CyclotomicRing
import FltRegular.NumberTheory.Different
import FltRegular.NumberTheory.Finrank
import FltRegular.NumberTheory.GaloisPrime
import FltRegular.NumberTheory.Hilbert90
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110 changes: 0 additions & 110 deletions FltRegular/NumberTheory/AuxLemmas.lean

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104 changes: 0 additions & 104 deletions FltRegular/NumberTheory/Different.lean

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10 changes: 5 additions & 5 deletions FltRegular/NumberTheory/GaloisPrime.lean
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@@ -1,11 +1,12 @@
import FltRegular.NumberTheory.AuxLemmas
import Mathlib.RingTheory.IntegralClosure.IntegralRestrict
import Mathlib.Data.Set.Card
import Mathlib.FieldTheory.PurelyInseparable
import Mathlib.Order.CompletePartialOrder
import Mathlib.RingTheory.DedekindDomain.Dvr
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.RingTheory.SimpleRing.Basic
import Mathlib.NumberTheory.RamificationInertia
import Mathlib.Algebra.Lie.OfAssociative

/-!
# Galois action on primes
Expand Down Expand Up @@ -237,15 +238,14 @@ lemma Ideal.ramificationIdxIn_bot : (⊥ : Ideal R).ramificationIdxIn S = 0 := b
lemma Ideal.inertiaDegIn_bot [Nontrivial R] [IsDomain S] [NoZeroSMulDivisors R S] [IsNoetherian R S]
[Algebra.IsIntegral R S] [H : (⊥ : Ideal R).IsMaximal] :
(⊥ : Ideal R).inertiaDegIn S = Module.finrank R S := by
delta inertiaDegIn
dsimp [inertiaDegIn]
rw [primesOver_bot]
have : ({⊥} : Set (Ideal S)).Nonempty := by simp
rw [dif_pos this, this.choose_spec]
have hR := not_imp_not.mp (Ring.ne_bot_of_isMaximal_of_not_isField H) rfl
have hS := isField_of_isIntegral_of_isField' (S := S) hR
letI : Field R := hR.toField
letI : Field S := hS.toField
have : IsIntegralClosure S R S := isIntegralClosure_self
rw [← Ideal.map_bot (f := algebraMap R S), ← finrank_quotient_map (R := R) (S := S) ⊥ R S]
exact inertiaDeg_algebraMap _ _

Expand All @@ -261,7 +261,7 @@ lemma Ideal.ramificationIdxIn_eq_ramificationIdx [IsGalois K L] (p : Ideal R) (P
rw [dif_pos this]
have ⟨σ, hσ⟩ := exists_comap_galRestrict_eq R K L S hP this.choose_spec
rw [← hσ]
exact Ideal.ramificationIdx_comap_eq (galRestrict R K L S σ) p P
exact Ideal.ramificationIdx_comap_eq (galRestrict R K L S σ) P

lemma Ideal.inertiaDegIn_eq_inertiaDeg [IsGalois K L] (p : Ideal R) (P : Ideal S)
(hP : P ∈ primesOver S p) [p.IsMaximal] :
Expand All @@ -271,7 +271,7 @@ lemma Ideal.inertiaDegIn_eq_inertiaDeg [IsGalois K L] (p : Ideal R) (P : Ideal S
rw [dif_pos this]
have ⟨σ, hσ⟩ := exists_comap_galRestrict_eq R K L S hP this.choose_spec
rw [← hσ]
exact Ideal.inertiaDeg_comap_eq (galRestrict R K L S σ) p P
exact Ideal.inertiaDeg_comap_eq p (galRestrict R K L S σ) P

open Module

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7 changes: 4 additions & 3 deletions FltRegular/NumberTheory/KummersLemma/Field.lean
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Expand Up @@ -101,9 +101,10 @@ lemma map_poly : (poly hp hζ u hcong).map (algebraMap (𝓞 K) K) =
include hu in
lemma irreducible_map_poly :
Irreducible ((poly hp hζ u hcong).map (algebraMap (𝓞 K) K)) := by
rw [map_poly, ← irreducible_taylor_iff (r := 1 / (ζ - 1))]
simp only [taylor, one_div, map_add, LinearMap.coe_mk, AddHom.coe_mk, pow_comp, sub_comp,
X_comp, C_comp, add_sub_cancel_right]
rw [map_poly]
refine Irreducible.of_map (f := algEquivAevalXAddC (1 / (ζ - 1))) ?_
simp only [one_div, map_add, algEquivAevalXAddC_apply, map_pow, map_sub, aeval_X, aeval_C,
algebraMap_eq, add_sub_cancel_right]
rw [← sub_neg_eq_add, ← (C : K →+* _).map_neg]
apply X_pow_sub_C_irreducible_of_prime hpri.out
intro b hb
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7 changes: 4 additions & 3 deletions FltRegular/NumberTheory/Unramified.lean
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@@ -1,6 +1,7 @@
import FltRegular.NumberTheory.GaloisPrime
import Mathlib.NumberTheory.KummerDedekind
import FltRegular.NumberTheory.Different
import Mathlib.RingTheory.DedekindDomain.Different

/-!
# Unramified extensions
Expand Down Expand Up @@ -166,8 +167,8 @@ lemma isUnramifiedAt_of_Separable_minpoly' [Algebra.IsSeparable K L]
have hxP : aeval x (derivative (minpoly R x)) ∈ P := by
have : differentIdeal R S ≤ P := by
rw [← Ideal.dvd_iff_le]
exact (dvd_pow_self _ H).trans (pow_sub_one_dvd_differentIdeal R S P _ hpbot
(Ideal.dvd_iff_le.mpr <| Ideal.le_pow_ramificationIdx (p := p) (f := algebraMap R S)))
exact (dvd_pow_self _ H).trans (pow_sub_one_dvd_differentIdeal R P _ hpbot <|
Ideal.dvd_iff_le.mpr <| Ideal.le_pow_ramificationIdx)
exact this (aeval_derivative_mem_differentIdeal R K L _ hx')
rw [← Ideal.Quotient.eq_zero_iff_mem, ← Ideal.Quotient.algebraMap_eq] at hxP

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4 changes: 2 additions & 2 deletions lake-manifest.json
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Expand Up @@ -5,7 +5,7 @@
"type": "git",
"subDir": null,
"scope": "leanprover-community",
"rev": "dc72dcdb8e97b3c56bd70f06f043ed2dee3258e6",
"rev": "eb6c831c05bc6ca6d37454ca97531a9b780dfcb5",
"name": "batteries",
"manifestFile": "lake-manifest.json",
"inputRev": "main",
Expand Down Expand Up @@ -75,7 +75,7 @@
"type": "git",
"subDir": null,
"scope": "",
"rev": "9d502188e7df20d93aded2b312b28259ff1da308",
"rev": "d27f22898a74975360dd1387155c6031b501a90b",
"name": "mathlib",
"manifestFile": "lake-manifest.json",
"inputRev": null,
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