On the $p$-adic distance between a point of finite order and a curve of genus higher or equal to two
| dc.creator | Rössler, Damian | |
| dc.date | 2008-04-23 | |
| dc.date | 2008-05-08 | |
| dc.date.accessioned | 2026-07-07T09:37:29Z | |
| dc.date.available | 2026-07-07T09:37:29Z | |
| dc.description | Let $A$ be an abelian variety over ${\bf C}_p$ ($p$ a prime number) and $V\hookrightarrow A$ a closed subvariety. The conjecture of Tate-Voloch predicts that the $p$-adic distance from a torsion point $T\not\in V({\bf C}_p)$ to the variety $V$ is bounded below by a strictly positive constant. This conjecture is proven by Hrushovski and Scanlon, when $A$ has a model over $\bar{\bf C}_p$. We give an explicit formula for this constant, in the case where $V$ is a curve embedded into its Jacobian and $V$ has a model over a number field. This explicit formula involves analytic and arakelovian invariants of the curve. | |
| dc.identifier | https://arxiv.org/abs/0804.3747 | |
| dc.identifier | http://arxiv.org/abs/0804.3747 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160473 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14G40 | |
| dc.title | On the $p$-adic distance between a point of finite order and a curve of genus higher or equal to two | |
| dc.type | text |