Mazur 13 port: mumfordIdeal_sq_eq_square_generator

Proved

MazurProof.N13MumfordFullKummerIdentityFiber.mumfordIdeal_sq_eq_square_generator

by xuanji · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

huang-flt-portmazur-full-torsionmazur-n13-portorder13

Supporting lemma mumfordIdeal_sq_eq_square_generator (namespace MazurProof.N13MumfordFullKummerIdentityFiber).

This lemma is one step of a machine-checked proof that the genus-two curve

Y^2 = X^6+4X^5+6X^4+2X^3+X^2+2X+1

(a model of $X_1(13)$ ) has no rational affine points other than the cusps $X\in\{0,-1\}$ , which gives the case $N=13$ of Mazur's torsion theorem. The proof is Xiang Huang's Lean development, ported to this Mathlib and split into one node per large lemma; definitions live in the layered entries MazurN13_L0, MazurN13_L1, ….

Preamble

import Mathlib
import Definitions.Def_MazurN13_L0

open MazurProof MazurProof.N13MumfordFullKummerIdentityFiber
open Polynomial
open SexticMumford
open scoped nonZeroDivisors
universe u
variable {K : Type u} [Field K]

Formal statement

theorem MazurProof.N13MumfordFullKummerIdentityFiber.mumfordIdeal_sq_eq_square_generator (C : SexticMumford.Model K) (a w L₀ : K[X]) (hcurve : C.f - L₀ ^ 2 = a * w) (haw : a ∣ w) (hbezout : ∃ A B E : K[X], A * a + B * (2 * L₀) + E * w = 1) : mumfordIdeal C a L₀ ^ 2 = mumfordIdeal C (a ^ 2) L₀ := by sorry

Source

Xiang Huang, FLT fork, https://github.com/xiangyazi24/FLT/blob/51bbb4f/FLT/Assumptions/MazurProof/N13MumfordFullKummerIdentityFiber.lean#L1532

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