Timeline for Smoothness of a morphism of smooth varieties with smooth fibres
Current License: CC BY-SA 4.0
9 events
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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 |