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May 2, 2018 at 13:18 comment added Axel Stäbler Possibly relevant: arxiv preprint, especially Corollary 5.6
Apr 30, 2018 at 20:11 comment added Jana @R.vanDobbendeBruyn The family $\pi$ is question is not smooth.
Apr 30, 2018 at 18:46 comment added R. van Dobben de Bruyn Note that this type of question is much easier if you replace '$X$ a regular scheme' by '$\pi$ a smooth morphism', because the latter is well-behaved in families. The statement for $\pi$ smooth follows from the case over $\operatorname{Spec} k$, because the smooth locus is open.
Apr 30, 2018 at 11:07 history edited Jana CC BY-SA 3.0
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Apr 30, 2018 at 9:12 history asked Jana CC BY-SA 3.0