Over rings of integers in number fields, finite flat linearly reductive subgroups of SL2 are exactly fppf local forms of μ_n, with finitely many GL2-conjugacy classes and controlled quotient singularities.
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An arithmetic analog of Klein's classification of finite subgroups of $\mathrm{SL}_2(\mathbb{C})$
Over rings of integers in number fields, finite flat linearly reductive subgroups of SL2 are exactly fppf local forms of μ_n, with finitely many GL2-conjugacy classes and controlled quotient singularities.