Curves of every genus with many points, I: Abelian and toric families
| dc.creator | Kresch, Andrew | |
| dc.creator | Wetherell, Joseph L. | |
| dc.creator | Zieve, Michael E. | |
| dc.date | 1999-12-09 | |
| dc.date | 2001-08-29 | |
| dc.date.accessioned | 2026-07-07T08:14:14Z | |
| dc.date.available | 2026-07-07T08:14:14Z | |
| dc.description | Let N_q(g) denote the maximal number of F_q-rational points on any curve of genus g over the finite field F_q. Ihara (for square q) and Serre (for general q) proved that limsup_{g-->infinity} N_q(g)/g > 0 for any fixed q. In their proofs they constructed curves with many points in infinitely many genera; however, their sequences of genera are somewhat sparse. In this paper, we prove that lim_{g-->infinity} N_q(g) = infinity. More precisely, we use abelian covers of P^1 to prove that liminf_{g-->infinity} N_q(g)/(g/log g) > 0, and we use curves on toric surfaces to prove that liminf_{g-->infty} N_q(g)/g^{1/3} > 0; we also show that these results are the best possible that can be proved with these families of curves. | |
| dc.description | LaTeX, 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/9912069 | |
| dc.identifier | http://arxiv.org/abs/math/9912069 | |
| dc.identifier | J. Algebra 250, no. 1 (2002), 353--370 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133050 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 11G20, 14G05, 14G15 | |
| dc.title | Curves of every genus with many points, I: Abelian and toric families | |
| dc.type | text |