Timeline for Intersection of curves in abelian varieties
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Oct 5, 2017 at 3:38 | comment | added | Vesselin Dimitrov | I believe boundedness should be expected in characteristic zero, but proving it might be difficult. There is a simpler problem in linear tori: If $X, Y \subset \mathbb{G}_{m/\mathbb{C}}^3$ are fixed curves, prove that there is an upper bound on the number of points that belong to both $X$ and $[n]Y+Q$, as $n \in \mathbb{Z}$ and $Q \in \mathbb{G}_m^3(\mathbb{C})$ vary in such a way that these curves have no component in common. The original problem may be reduced to this kind of statement inside an abelian variety, replacing $[n]$ by the isogenies of $A$. | |
| Oct 5, 2017 at 3:19 | comment | added | Will Sawin | If the Manin-Mumford conjecture were false, a similar technique would work in characteristic zero, using multiplication by $1+n!$. So any technique to prove boundedness would have to be strong enough to prove Manin-Mumford. Don't existing proofs of Manin-Mumford use heavily the Galois action on the torsion points, which seems not usefully available here? | |
| Oct 5, 2017 at 2:23 | history | edited | Felipe Voloch | CC BY-SA 3.0 |
added 349 characters in body
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| Oct 4, 2017 at 20:08 | history | asked | Felipe Voloch | CC BY-SA 3.0 |