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Apr 29, 2021 at 8:36 vote accept Mikhail Borovoi
Apr 29, 2021 at 8:13 answer added Francesco Polizzi timeline score: 1
Apr 29, 2021 at 8:04 history edited Francesco Polizzi CC BY-SA 4.0
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Apr 27, 2021 at 19:42 comment added Mikhail Borovoi Thank you, @FrancescoPolizzi! I did know the book of Matsumura, but not the text of Ravi Vakil....
Apr 27, 2021 at 18:51 comment added Laurent Moret-Bailly Another reference: Matsumura, Commutative Ring Theory, Theorem 23.1.
Apr 27, 2021 at 18:44 comment added Francesco Polizzi If $f$ is smooth, then $f$ is flat and the fibres are automatically smooth and equidimensional, see [Vakil, thm. 25.2.2]. This provides one implication of your desired statement. The converse implication is [Vakil, Exercise 25.2.F (a)].
Apr 27, 2021 at 18:15 history edited Mikhail Borovoi CC BY-SA 4.0
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Apr 27, 2021 at 18:08 history edited Mikhail Borovoi CC BY-SA 4.0
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Apr 27, 2021 at 18:01 history asked Mikhail Borovoi CC BY-SA 4.0