Timeline for Is there a version of the valuative criteria for separateness/properness for varieties?
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 15, 2021 at 2:09 | answer | added | Joel Kamnitzer | timeline score: 5 | |
| Oct 21, 2009 at 1:31 | vote | accept | Joel Kamnitzer | ||
| Oct 21, 2009 at 1:31 | vote | accept | Joel Kamnitzer | ||
| Oct 21, 2009 at 1:31 | |||||
| Oct 17, 2009 at 12:44 | history | edited | Joel Kamnitzer | CC BY-SA 2.5 |
added 179 characters in body
|
| Oct 17, 2009 at 7:10 | answer | added | Anton Geraschenko | timeline score: 2 | |
| Oct 17, 2009 at 6:48 | comment | added | Anton Geraschenko | ... of course you're also allowing the residue field to be a finite extension of k. | |
| Oct 17, 2009 at 6:36 | comment | added | Anton Geraschenko | A variety is usually assumed to be reduced, irreducible (sometimes), separated (I assume you don't want this), and finite type over a field k. Are there any other conditions you're imposing? Supposing we know what a variety is, it's clear that if X is separated/proper, then it satisfies your condition (it's weaker than the usual valuative criteria). So it sounds like your question is, "is it enough to check DVRs whose residue field is k and whose field of fractions has transcendence degree 1 over k?" Do I have that right? | |
| Oct 17, 2009 at 5:39 | answer | added | Greg Stevenson | timeline score: 4 | |
| Oct 17, 2009 at 5:21 | comment | added | user332 | Doesn't the definition of a variety require it to be separated? | |
| Oct 17, 2009 at 3:43 | comment | added | Theo Johnson-Freyd | I don't know any algebraic geometry, but I expect that the discussion at: mathoverflow.net/questions/493/… may have some insight. | |
| Oct 17, 2009 at 2:36 | history | asked | Joel Kamnitzer | CC BY-SA 2.5 |