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FLT/Basic/Reductions.lean

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import Mathlib.Data.PNat.Basic
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import Mathlib.NumberTheory.FLT.Four
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import Mathlib.NumberTheory.FLT.Three
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import Mathlib.Tactic
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import Mathlib.AlgebraicGeometry.EllipticCurve.Affine
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import Mathlib.RepresentationTheory.Basic
@@ -49,12 +50,6 @@ theorem PNat.pow_add_pow_ne_pow_of_FermatLastTheorem :
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specialize h₁ n h₂ a b c (by simp) (by simp) (by simp)
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assumption_mod_cast
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/-- Fermat's Last Theorem is true when n = 3. -/
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lemma fermatLastTheoremThree : FermatLastTheoremFor 3 := sorry
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-- This is proved in the FLT-regular project (https://github.com/leanprover-community/flt-regular/blob/861b7df057140b45b8bb7d30d33426ffbbdda52b/FltRegular/FltThree/FltThree.lean#L698)
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-- and the FLT3 project (https://github.com/riccardobrasca/flt3).
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-- The way to turn this node green is to port this latter one to mathlib so we can use it here.
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namespace FLT
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/-- If Fermat's Last Theorem is true for primes `p ≥ 5`, then FLT is true. -/

FLT/GlobalLanglandsConjectures/GLnDefs.lean

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@@ -11,7 +11,7 @@ import Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation
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import Mathlib.Geometry.Manifold.Instances.UnitsOfNormedAlgebra
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import Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Basic
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import Mathlib.LinearAlgebra.UnitaryGroup
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import Mathlib.RepresentationTheory.FdRep
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import Mathlib.RepresentationTheory.FDRep
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import Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing
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import Mathlib.Topology.LocallyConstant.Basic
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@@ -278,7 +278,7 @@ structure preweight (n : ℕ) where
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open CategoryTheory
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noncomputable def preweight.fdRep (n : ℕ) (w : preweight n) :
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FdRep ℂ (orthogonalGroup (Fin n) ℝ) where
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FDRep ℂ (orthogonalGroup (Fin n) ℝ) where
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V := FGModuleCat.of ℂ (Fin w.d → ℂ)
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ρ := {
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toFun := fun A ↦ {

blueprint/src/chapter/ch02reductions.tex

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There are no solutions in positive integers to $a^3+b^3=c^3$.
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\end{lemma}
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\begin{proof}
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\leanok
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A proof has been formalised in Lean in the FLT-regular project \href{https://github.com/leanprover-community/flt-regular/blob/861b7df057140b45b8bb7d30d33426ffbbdda52b/FltRegular/FltThree/FltThree.lean#L698}{\underline{here}}.
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Another proof has been formalised in Lean in the FLT3 project \href{https://github.com/riccardobrasca/flt3}{\underline{here}} by a team from the Lean For the Curious Mathematician conference held in Luminy in March 2024
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(its dependency graph can be visualised \href{https://pitmonticone.github.io/FLT3/blueprint/dep_graph_document.html}{\underline{here}}).
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To get this node green, this latter proof needs to be upstreamed to mathlib. This is currently work in progress by the same team.
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\end{proof}
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\begin{corollary}\label{FLT.of_p_ge_5}\lean{FLT.of_p_ge_5}\leanok If there is a counterexample to Fermat's Last Theorem, then there is a counterexample $a^p+b^p=c^p$ with $p$ prime and $p\geq 5$.

blueprint/src/chapter/ch07exampleGLn.tex

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\label{AutomorphicForm.GLn.AutomorphicFormForGLnOverQ}
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\lean{AutomorphicForm.GLn.AutomorphicFormForGLnOverQ}
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\uses{AutomorphicForm.GLn.IsSmooth, AutomorphicForm.GLn.IsSlowlyIncreasing,
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AutomorphicForm.GLn.weight, instCentreAction}
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AutomorphicForm.GLn.Weight, instCentreAction}
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A smooth function $f:\GL_n(\A_{\Q}^f)\times\GL_n(\R)\to\bbC$ is
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an $O_n(\R)$-\emph{automorphic form} on $\GL_n(\A_{\Q})$ if it satisfies the following
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five conditions.

lake-manifest.json

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"type": "git",
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"subDir": null,
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"scope": "leanprover-community",
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lean-toolchain

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leanprover/lean4:v4.10.0-rc1
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leanprover/lean4:v4.10.0-rc2

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