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Apr 15, 2017 at 17:52 comment added R. van Dobben de Bruyn At the very least, you'll want to assume that the fibres are geometrically irreducible, to prevent examples like field extensions. But it seems that under those assumptions, it should indeed be ok.
Apr 15, 2017 at 7:04 history edited Friedrich Knop CC BY-SA 3.0
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Apr 15, 2017 at 6:16 history answered Friedrich Knop CC BY-SA 3.0