Exceptional covers and bijections on rational points

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dc.creatorGuralnick, Robert M.
dc.creatorTucker, Thomas J.
dc.creatorZieve, Michael E.
dc.date2005-11-10
dc.date2007-05-15
dc.date.accessioned2026-07-07T09:42:57Z
dc.date.available2026-07-07T09:42:57Z
dc.descriptionWe show that if f: X --> Y is a finite, separable morphism of smooth curves defined over a finite field F_q, where q is larger than an explicit constant depending only on the degree of f and the genus of X, then f maps X(F_q) surjectively onto Y(F_q) if and only if f maps X(F_q) injectively into Y(F_q). Surprisingly, the bounds on q for these two implications have different orders of magnitude. The main tools used in our proof are the Chebotarev density theorem for covers of curves over finite fields, the Castelnuovo genus inequality, and ideas from Galois theory.
dc.description19 pages; various minor changes to previous version. To appear in International Mathematics Research Notices
dc.identifierhttps://arxiv.org/abs/math/0511276
dc.identifierhttp://arxiv.org/abs/math/0511276
dc.identifierInternat. Math. Res. Notices 2007; Vol. 2007: article ID rnm004
dc.identifierdoi:10.1093/imrn/rnm004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/162375
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject11G20, 14G15
dc.titleExceptional covers and bijections on rational points
dc.typetext

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