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Drinfeld modules and algebraic curves with many rational points. (Modules de Drinfeld et courbes algébriques ayant beaucoup de points rationnels.) (French) Zbl 0853.11051

In this note global fields of positive characteristics (with constant field \(\mathbb{F}_q\)) are constructed such that the corresponding projective smooth algebraic curves admit many rational points over \(\mathbb{F}_q\). Methods of constructions come from those of the arithmetic in positive characteristic, especially from the construction of the ray class field by Drinfeld modules of rank 1, given by D. R. Hayes [Adv. Math., Suppl. Stud. 6, 173-217 (1979; Zbl 0476.12010)].

MSC:

11G09 Drinfel’d modules; higher-dimensional motives, etc.
14L05 Formal groups, \(p\)-divisible groups

Citations:

Zbl 0476.12010
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