Non-Cyclic Subgroups of Jacobians of Genus Two Curves
| dc.creator | Ravnshoj, Christian Robenhagen | |
| dc.date | 2008-01-18 | |
| dc.date.accessioned | 2026-07-07T08:55:18Z | |
| dc.date.available | 2026-07-07T08:55:18Z | |
| dc.description | Let E be an elliptic curve defined over a finite field. Balasubramanian and Koblitz have proved that if the l-th roots of unity m_l is not contained in the ground field, then a field extension of the ground field contains m_l if and only if the l-torsion points of E are rational over the same field extension. We generalize this result to Jacobians of genus two curves. In particular, we show that the Weil- and the Tate-pairing are non-degenerate over the same field extension of the ground field. From this generalization we get a complete description of the l-torsion subgroups of Jacobians of supersingular genus two curves. In particular, we show that for l>3, the l-torsion points are rational over a field extension of degree at most 24. | |
| dc.identifier | https://arxiv.org/abs/0801.2835 | |
| dc.identifier | http://arxiv.org/abs/0801.2835 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146226 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G20 (Primary); 11T71, 14G50, 14H45 (Secondary) | |
| dc.title | Non-Cyclic Subgroups of Jacobians of Genus Two Curves | |
| dc.type | text |