Timeline for Smooth proper schemes over rings of integers with points everywhere locally
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 22, 2022 at 8:13 | history | edited | CommunityBot |
replaced http://math.uga.edu/~pete with http://alpha.math.uga.edu/~pete
|
|
| Jan 10, 2010 at 12:28 | vote | accept | Chandan Singh Dalawat | ||
| Nov 27, 2011 at 8:42 | |||||
| Jan 8, 2010 at 10:42 | comment | added | Chandan Singh Dalawat | That's very nice, Pete; the question seems to have been tailor-made for you! I'm tempted to "accept" your answer, but perhaps we should wait for someone to write down an explicit equation of a genus-$1$ curve $C$ over a quadratic field $K$ whose jacobian $J$ has good reduction everywhere and such that $[C]$ is an order-$2$ element of $\operatorname{Sha}(J,K)$. It would have the same appeal as Selmer's example ($3x^3+4y^3+5z^3=0$) or Tate's example ($y^2+xy+\varepsilon^2y=x^3$). | |
| Jan 8, 2010 at 9:03 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
edited body
|
| Jan 8, 2010 at 9:03 | comment | added | Pete L. Clark | My choice of Tate's example was made independently of Chandan's comment above: it's just a coincidence. Anyway, there are plenty of other examples, probably including some which have nontrivial Sha over the ground field. | |
| Jan 8, 2010 at 8:54 | history | answered | Pete L. Clark | CC BY-SA 2.5 |