Timeline for Functorial criterion for local complete intersection morphisms?
Current License: CC BY-SA 4.0
8 events
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| Sep 7, 2022 at 14:57 | history | edited | Matthieu Romagny | CC BY-SA 4.0 |
clarified lci versus syntomic
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| Sep 7, 2022 at 14:55 | comment | added | Matthieu Romagny | Thanks for these clarifications, I'm editing the question to focus on syntomic morphisms then. | |
| Sep 7, 2022 at 11:37 | comment | added | Jason Starr | The OP states that his morphism is flat. There is a valuative criterion for flatness. For a flat morphism, the morphism is LCI if and only if the cotangent complex is bounded. At least in the category of dg schemes / rings, there is a universal property of the cotangent complex that can be used to write a functorial property for boundedness of the cotangent complex. | |
| Sep 7, 2022 at 11:14 | comment | added | Marc Hoyois | @abx Not so, EGA only defines the lci condition for flat morphisms, but does not say that lci morphisms should be flat, and SGA has the general definition. | |
| Sep 7, 2022 at 9:58 | comment | added | abx | It does according to EGA (IV, Def. 19.3.6), and also SGA 7, Exp. VIII, Def. 1.1. | |
| Sep 7, 2022 at 9:49 | comment | added | R. van Dobben de Bruyn | Unlike syntomic, the notion of lci morphism usually does not include flatness, as far as I'm aware. See for instance Tags 069F and 069K. | |
| Sep 7, 2022 at 9:26 | history | edited | Matthieu Romagny | CC BY-SA 4.0 |
Added details, in particular added definition of local complete intersection morphism
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| Sep 7, 2022 at 9:01 | history | asked | Matthieu Romagny | CC BY-SA 4.0 |