A Formalization of Dedekind Domains and Class Groups of Global Fields

Abstract

Dedekind domains and their class groups are notions in commutative algebra that are essential in algebraic number theory. We formalized these structures and several fundamental properties, including number-theoretic finiteness results for class groups, in the Lean prover as part of the mathlib mathematical library. This paper describes the formalization process, noting the idioms we found useful in our development and mathlib’s decentralized collaboration processes involved in this project.