The rank of elliptic surfaces in unramified abelian towers
| dc.creator | Silverman, Joseph H. | |
| dc.date | 2003-05-01 | |
| dc.date.accessioned | 2026-07-07T08:14:24Z | |
| dc.date.available | 2026-07-07T08:14:24Z | |
| dc.description | Let E --> C be an elliptic surface defined over a number field K. For each finite covering C' --> C defined over K, let E' --> C' be the pullback. We give a strong upper bound for the rank of E'(C'/K) in the case that C' --> C is an unramified abelian covering and under the assumption that the Tate conjecture is true for the surface E'/K. In the case that C is an elliptic curve and the map C'=C --> C is the multiplication-by-n map, the rank of E'(C'/K) is O(n^e) for every e > 0, which may be compared with the elementary bound of O(n^2). | |
| dc.identifier | https://arxiv.org/abs/math/0305028 | |
| dc.identifier | http://arxiv.org/abs/math/0305028 | |
| dc.identifier | J. Reine Angew. Math. 577 (2004), 153--169. (MR2108217) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133110 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14G25 (Primary) 11G05, 14J27, 14J20 (Secondary) | |
| dc.title | The rank of elliptic surfaces in unramified abelian towers | |
| dc.type | text |