No abstract

Pour une représentation galoisienne diédrale en caractéristique ℓ on établit (sous certaines hypothèses) l'existence d'une newform à multiplication complexe, dont on contrôle le poids, le niveau et le caractère, telle que la représentation ℓ-adique associée est congrue modulo ℓ à celle de départ.Given a dihedral Galois representation in characteristic ℓ, we establish (under some assumption) the existence of a CM newform, whose weight, level and Nebentypus we pin down, such that its ℓ-adic representation is congruent modulo ℓ to the one we started with.

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 mathematical library. This paper describes the formalization process, noting the idioms we found useful in our development and ’s decentralized collaboration processes involved in this project.