Arithmetic on Elliptic Threefolds
| dc.creator | Wazir, Rania | |
| dc.date | 2001-12-23 | |
| dc.date.accessioned | 2026-07-07T04:45:28Z | |
| dc.date.available | 2026-07-07T04:45:28Z | |
| dc.description | In a recent paper, Rosen and Silverman showed that Tate's conjecture on the order of vanishing of L(E,s) implies Nagao's formula, which gives the rank of an elliptic surface in terms of a weighted average of fibral Frobenius trace values. The aim of this article is to extend their result to the case of elliptic threefolds, and deduce, from Tate's conjecture, a Nagao-type formula for the rank of an elliptic threefold E. This will require a two-pronged approach: on the one hand, we need some cohomological results in order to derive a Shioda-Tate-like formula for elliptic threefolds; on the other, we compute an "average" number of rational points on the singular fibers and relate this to the action of Galois on those fibers. | |
| dc.description | 34 pages | |
| dc.identifier | https://arxiv.org/abs/math/0112259 | |
| dc.identifier | http://arxiv.org/abs/math/0112259 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62966 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11D45; 14D06 | |
| dc.title | Arithmetic on Elliptic Threefolds | |
| dc.type | text |