New York Journal of Mathematics
Volume 19 (2013) 131-144


Amílcar Pacheco and Fabien Pazuki

Bounds for the number of rational points on curves over function fields

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Published: April 29, 2013
Keywords: Abelian varieties, rational points, curves, function fields
Subject: 11G35, 11R58, 14G40, 14G25, 14H05

We provide an upper bound for the number of rational points on a nonisotrivial curve defined over a one variable function field over a finite field. The bound only depends on the curve and the field, and not on the Jacobian variety of the curve.


The first author wishes to thank the Institut de Mathématiques de Jussieu, Paris, for its support during his sabbatical. This stay had also the support of CNPq (Brazil), CNRS (France) and Paris Science Foundation. Both authors would like to thank Université Bordeaux 1, ANR-10-BLAN-0115 Hamot and ANR-10-JCJC-0107 Arivaf (France).

Author information

Amílcar Pacheco:
Universidade Federal do Rio de Janeiro, Instituto de Matemática, Av. Athos da Silveira Ramos 149, CT, Bl. C, Cidade Universitária, Ilha do Fundão, Caixa Postal 68530, 21941-909 Rio de Janeiro, RJ, Brasil

Fabien Pazuki:
Institut de Mathématiques de Bordeaux, Université Bordeaux I, 351, cours de la Libération, 33405 Talence, France