Timeline for Excellent schemes
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 21, 2015 at 18:11 | comment | added | R3D3 | ...(cont'ed): Your talking about proofs of results without knowing what results you are talking about seems smug at best. If you know so well, you could suggest a particular result where it is nicely demonstrated how excellence is used. What you are currently doing is BS. | |
| Jan 21, 2015 at 18:10 | comment | added | R3D3 | @user74230: this is a fruitless discussion, so this is my last comment on it: I did not say I read those proofs and unfortunately I do not have time to read them carefully. I looked at some of them, but mostly just scanned them, and based on that it was not clear where they use excellence. In fact, I venture to say that some, actually many, authors do not point out where they use an assumption and this is especially true for excellence.... (cont'ed) | |
| Jan 21, 2015 at 8:40 | comment | added | user74230 | @R3D3: You say in the question that you have "noticed that many results" assume excellence, so I assumed you have a big supply of results using excellence that you already care about. The only way I ever grokked this topic was to see how it is used in proofs of things I already cared about. So my advice is not flippant and is based on exactly what I did myself. Pick at random among the "many" results you say you have noticed, and as you read the proofs using excellence you will understand what its purpose is (especially to address Question 1). | |
| Jan 21, 2015 at 7:46 | vote | accept | R3D3 | ||
| Jan 21, 2015 at 7:25 | answer | added | Fred Rohrer | timeline score: 1 | |
| Jan 21, 2015 at 7:18 | comment | added | R3D3 | @user74230: Thank you, but this isn't really helpful. You are saying I should do what I am asking help to do. I rarely work with situations where this matters and I asked the question so I could get some guidance in where to look. Suggesting to look at many results is not helpful at all. | |
| Jan 21, 2015 at 7:14 | comment | added | R3D3 | @FredRohrer: Thanks for that suggestion. If you would add it as an answer, I am happy to accept it. | |
| Jan 17, 2015 at 14:02 | comment | added | user74230 | There are non-excellent dvr's in positive characteristic (though every complete local noetherian ring and Dedekind domain of char. 0 is excellent). It is unwise to "assume that every scheme I ever work with is excellent". It is better to understand how to reduce problems to the excellent case (or when excellence is truly a necessary assumption), and more importantly from the proofs of many results you have read you can learn the answer to Question 1 (e.g., passage to various kinds of completion is well-behaved for properties like reducedness, normality, etc. under excellence assumptions). | |
| Jan 17, 2015 at 7:25 | comment | added | Fred Rohrer | Dear R3D3, have you read EGA IV.7.8 yet? | |
| Jan 17, 2015 at 6:59 | review | First posts | |||
| Jan 17, 2015 at 8:11 | |||||
| Jan 17, 2015 at 6:56 | history | asked | R3D3 | CC BY-SA 3.0 |