Modular Categories Associated to Unipotent Groups

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Let G be a unipotent algebraic group over an algebraically closed field k of characteristic p > 0 and let l be a prime different from p. Let e be a minimal idempotent in DG(G), the braided monoidal category of G-equivariant (under conjugation action) Qₗ-complexes on G. We can associate to G and e a modular category MG,ₑ. In this article, we prove that the modular categories that arise in this way from unipotent groups are precisely those in the class Cₚ±.