Remark 39.8.3. Any group scheme over a field of characteristic $0$ is reduced, see [I, Theorem 1.1 and I, Corollary 3.9, and II, Theorem 2.4, Perrin-thesis] and also [Proposition 4.2.8, Perrin]. This was a question raised in [page 80, Oort]. We have seen in Lemma 39.8.2 that this holds when the group scheme is locally of finite type.

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