Geodesic
Rational points of algebraic curves
Matematičeskie zametki, Tome 18 (1975) no. 6, pp. 903-908 
V. A. Dem'yanenko. Rational points of algebraic curves. Matematičeskie zametki, Tome 18 (1975) no. 6, pp. 903-908. http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a12/
@article{MZM_1975_18_6_a12,
     author = {V. A. Dem'yanenko},
     title = {Rational points of algebraic curves},
     journal = {Matemati\v{c}eskie zametki},
     pages = {903--908},
     year = {1975},
     volume = {18},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a12/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that the number of $k$-points of certain curves of genus $g>1$ is finite.