Heegner points and the rank of elliptic curves over large extensions of global fields
| dc.creator | Breuer, Florian | |
| dc.creator | Im, Bo-Hae | |
| dc.date | 2006-04-05 | |
| dc.date | 2006-04-06 | |
| dc.date.accessioned | 2026-07-07T07:10:33Z | |
| dc.date.available | 2026-07-07T07:10:33Z | |
| dc.description | Let k be a global field, $\bar{k}$ a separable closure of k, and $G_k$ the absolute Galois group $\Gal(\bar{k}/k)$ of $\bar{k}$ over k. For every g in $G_k$, let $\bar{k}^g$ be the fixed subfield of $\bar{k}$ under g. Let E/k be an elliptic curve over k. We show that for each g in $G_k$, the Mordell-Weil group $E(\bar{k}^g)$ has infinite rank in the following two cases. Firstly when k is a global function field of odd characteristic and E is parametrized by a Drinfeld modular curve, and secondly when k is a totally real number field and E/k is parametrized by a Shimura curve. In both cases our approach uses the non-triviality of a sequence of Heegner points on E defined over ring class fields. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0604107 | |
| dc.identifier | http://arxiv.org/abs/math/0604107 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111455 | |
| dc.subject | Number Theory | |
| dc.subject | 11G05 | |
| dc.title | Heegner points and the rank of elliptic curves over large extensions of global fields | |
| dc.type | text |