Open Research Index

Global class field theory in Lean 4.35.0-rc2

Naganori Yamaguchi

Palomar Registrypalomar/PALOMAR-2026-09-28-000001Sep 28, 2026math.NTscore 0

For every finite abelian extension L/K of number fields, the idèle class group C_K modulo the image of the idèle-class norm from C_L is isomorphic as a topological multiplicative group to Gal(L/K). The Challenge defines the norm as the determinant on the relative adèle algebra and descends it through principal idèles; the included ClassFieldTheory development supplies the proof of the resulting reciprocity theorem.

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