Curves of every genus with many points, II: Asymptotically good families

Simple item page
dc.creatorElkies, Noam D.
dc.creatorHowe, Everett W.
dc.creatorKresch, Andrew
dc.creatorPoonen, Bjorn
dc.creatorWetherell, Joseph L.
dc.creatorZieve, Michael E.
dc.date2002-08-08
dc.date.accessioned2026-07-07T04:50:07Z
dc.date.available2026-07-07T04:50:07Z
dc.descriptionWe resolve a 1983 question of Serre by constructing curves with many points of every genus over every finite field. More precisely, we show that for every prime power q there is a positive constant c_q with the following property: for every non-negative integer g, there is a genus-g curve over F_q with at least c_q * g rational points over F_q. Moreover, we show that there exists a positive constant d such that for every q we can choose c_q = d * (log q). We show also that there is a constant c > 0 such that for every q and every n > 0, and for every sufficiently large g, there is a genus-g curve over F_q that has at least c*g/n rational points and whose Jacobian contains a subgroup of rational points isomorphic to (Z/nZ)^r for some r > c*g/n.
dc.descriptionLaTeX, 18 pages
dc.identifierhttps://arxiv.org/abs/math/0208060
dc.identifierhttp://arxiv.org/abs/math/0208060
dc.identifierDuke Math. J. 122, no. 2 (2004), 399--422
dc.identifierdoi:10.1215/S0012-7094-04-12224-9
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64679
dc.subjectAlgebraic Geometry
dc.subjectNumber Theory
dc.subject14G05 (Primary) 11G20, 14G15 (Secondary)
dc.titleCurves of every genus with many points, II: Asymptotically good families
dc.typetext

Files

Collections

arXiv