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[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.

[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.

[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.

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[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.