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added 39 characters in body

edited Jul 21, 2012 at 18:58

[Assume the group schemes are reduced. [Görtz-Wedhorn], Theorem 14.5 gives generic flatness, and $\pi: G \to G/H$ is a homogeneous space ([Borel], LAG §6). For surjectivity, see [Borel], LAG §6.

answered Jul 21, 2012 at 16:53

user19475