Timeline for Sections of infinite order of elliptic surfaces
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 3, 2020 at 8:16 | comment | added | Pat | @VesselinDimitrov Thank you for this. Can you make this into an answer? | |
| Apr 19, 2020 at 6:54 | comment | added | Vesselin Dimitrov | Yes, there is are infinitely many such special parameters $P$ at which $\sigma(P)$ becomes torsion in its fibre. Moreover, all large enough orders are realizable for the torsion point. This comes by a version of the implicit function theorem. When the data is over the algebraic numbers, one further knows that these special parameters $P$ are a set of bounded height (so they are rather sparse). See Masser and Zannier's paper Torsion anomalous points and families of elliptic curves and, for a generalization, Prop. 3.1 in Habegger's paper Special points on fibered powers of elliptic surfaces. | |
| Apr 18, 2020 at 22:04 | history | asked | Pat | CC BY-SA 4.0 |