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Nombres de points des courbes algébriques sur \(F_ q\). (French) Zbl 0538.14016

Sémin. Théor. Nombres, Univ. Bordeaux I 1982-1983, Exp. No. 22, 8 p. (1983).
The author gives an overview concerning upper bounds for the numbers of rational points on a curve of genus g, over a finite field of q elements. In general one has the bound given by Weil’s theorem. There are more precise results of the following nature: (i) asymptotic results: Fix q, and let \(g\to \infty\); (ii) results for \(q=2\); (iii) results for \(g=1,2,3\).
Reviewer: G.Faltings

MSC:

14G15 Finite ground fields in algebraic geometry
14G05 Rational points
14H45 Special algebraic curves and curves of low genus
14N10 Enumerative problems (combinatorial problems) in algebraic geometry