Timeline for Simply connected quasi-projective varieties in positive characteristic
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 30, 2010 at 18:28 | vote | accept | Lars | ||
| Feb 22, 2010 at 14:43 | answer | added | Qing Liu | timeline score: 10 | |
| Feb 22, 2010 at 12:48 | comment | added | David E Speyer | Technical point: I should have asked for the bigger variety to be regular. | |
| Feb 22, 2010 at 12:31 | comment | added | Pete L. Clark | @DS: Grothendieck's specialization theorem applies to any projective variety which lifts to characteristic $0$. So for instance $\mathbb{P}^2$ is simply connected in all characteristics. So based on what you say (which I haven't seen before but sounds good to me), $\mathbb{P}^2$ minus a point is an example. | |
| Feb 22, 2010 at 12:29 | comment | added | Frank | In fact David's comment is SGA1 Corollary X.3.3 and has now reminded me of an old question of mine at mathoverflow.net/questions/5375/… | |
| Feb 22, 2010 at 12:21 | comment | added | David E Speyer | I am fairly sure that removing a codimension $2$ subvariety from a projective variety doesn't change the fundamental group. So I can take any projective example of dimension $2$ or greater and make it nonprojective by yanking out a point. | |
| Feb 22, 2010 at 12:17 | answer | added | Pete L. Clark | timeline score: 3 | |
| Feb 22, 2010 at 12:17 | answer | added | Frank | timeline score: 3 | |
| Feb 22, 2010 at 12:01 | history | edited | Lars | CC BY-SA 2.5 |
added 15 characters in body
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| Feb 22, 2010 at 11:59 | comment | added | Pete L. Clark | Note that any projective variety is quasi-projective. A comparison theorem of Grothendieck gives many examples of projective varieties in positive characteristic with trivial etale fundamental group. So probably you wish to amend your question slightly? | |
| Feb 22, 2010 at 11:59 | answer | added | David E Speyer | timeline score: 1 | |
| Feb 22, 2010 at 11:54 | history | asked | Lars | CC BY-SA 2.5 |