Timeline for Why are principal ideal domains and Dedekind domains prominent, but I always seem to see Noetherian rings rather than Noetherian domains?
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| Jun 22, 2022 at 8:14 | history | edited | CommunityBot |
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| Dec 19, 2010 at 9:50 | comment | added | Pete L. Clark | Okay, B -- I looked in Szamuely's notes instead of BLR for the definition. But either way the definition forces a connected, affine Dedekind scheme to be the spectrum of a domain. The definition is not a Noetherian Prufer ring -- that's my point. | |
| Dec 19, 2010 at 9:11 | comment | added | BCnrd | Au contraire, Pete. Dedekind schemes should not be assumed to be connected. It is a nuisance to require connectedness when doing etale descent (since the relevant fiber products are typically disconnected, even when the pieces are). This is the reason that connectedness is not required in the book "Neron Models". Yeah, a purely technical reason. But it's just like the way we don't require reductive groups to be connected and find ourselves saying "connected reductive" all the time...because on those occasions when connectedness is lost, it's still useful to apply parts of the theory. | |
| Dec 19, 2010 at 7:31 | history | answered | Pete L. Clark | CC BY-SA 2.5 |