Timeline for Smooth proper schemes over rings of integers with points everywhere locally
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Jan 8, 2010 at 13:54 | comment | added | Pete L. Clark | In fact this was already explained by Poonen in a "motivational comment" to his question linked to above. | |
| Jan 8, 2010 at 12:18 | comment | added | Chandan Singh Dalawat | Put another way, the only smooth proper curve over $\mathbb{Q}$ which has good reduction everywhere is $\mathbb{P}_1$. | |
| Jan 8, 2010 at 11:44 | comment | added | David E Speyer | That doesn't work. If f:C -> Z is a curve of genus zero, then omega_{C/Z}^{-1} has degree 2 and f^*(omega_{C/Z}^{-1}) is a free Z module of rank 3. (Locally free over a general base, but Z is a PID.) So C can be written as a conic in P^2_{Z}. The Hasse principle applies to conics. | |
| Jan 8, 2010 at 11:35 | history | answered | Hagen | CC BY-SA 2.5 |