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Dec 4, 2022 at 13:44 comment added Anonymous I think you could choose an absolute integral closure $R \to R^+$, which is necessarily faithfully flat, and then compare your question for $R$ and $R^+$ to get the desired flatness since $\text{Frob}:R^+/\pi \to R^+/\pi^p$ is an isomorphism.
Dec 3, 2022 at 23:00 history edited LSpice CC BY-SA 4.0
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Dec 3, 2022 at 22:33 history asked skd CC BY-SA 4.0