On the nonexistence of certain curves of genus two
| dc.creator | Howe, Everett W. | |
| dc.date | 2002-01-31 | |
| dc.date.accessioned | 2026-07-07T04:46:13Z | |
| dc.date.available | 2026-07-07T04:46:13Z | |
| dc.description | We prove that if q is a power of an odd prime then there is no genus-2 curve over F_q whose Jacobian has characteristic polynomial of Frobenius equal to x^4 + (2-2q)x^2 + q^2. Our proof uses the Brauer relations in a biquadratic extension of Q to show that every principally polarized abelian surface over F_q with the given characteristic polynomial splits over F_{q^2} as a product of polarized elliptic curves. | |
| dc.description | LaTeX, 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0201311 | |
| dc.identifier | http://arxiv.org/abs/math/0201311 | |
| dc.identifier | Compos. Math. 140 (2004) 581--592 | |
| dc.identifier | doi:10.1112/S0010437X03000757 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63243 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G20 (Primary); 11G10, 11R65, 14G15, 14H25 (Secondary) | |
| dc.title | On the nonexistence of certain curves of genus two | |
| dc.type | text |