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The global Kronecker–Weber theorem in Lean 4

Naganori Yamaguchi

Palomar Registrypalomar/PALOMAR-2026-09-05-000006Sep 5, 2026math.NTscore 0

This project formalizes the global Kronecker–Weber theorem in Lean 4: every finite abelian extension of the rational numbers embeds into a cyclotomic field. For a number field L that is abelian Galois over the rationals, the selected declaration gives a positive integer n and a rational algebra embedding from L into CyclotomicField n ℚ. The proof is supplied by the ClassFieldTheory library at a fixed commit, using Lean 4.33.0 and Mathlib.

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