Trivial points on towers of curves
Journal de théorie des nombres de Bordeaux, Volume 25 (2013) no. 2, p. 477-498

In order to study the behavior of the points in a tower of curves, we introduce and study trivial points on towers of curves, and we discuss their finiteness over number fields. We relate the problem of proving that the only rational points are the trivial ones at some level of the tower, to the unboundeness of the gonality of the curves in the tower, which we show under some hypothesis.

Afin d’étudier le comportement des points dans une tour de courbes, nous introduisons et étudions les points triviaux sur les tours de courbes, et nous discutons de leur finitude sur les corps de nombres. Nous relions le problème de prouver que les seuls points rationnels sont les points triviaux à un certain niveau de la tour à la non-existence d’une borne de la gonalité des courbes de la tour, que nous démontrons sous certaines hypothèses.

DOI : https://doi.org/10.5802/jtnb.845
Classification:  11G30,  11G20,  11B39,  11D45,  14G25
@article{JTNB_2013__25_2_477_0,
     author = {Xarles, Xavier},
     title = {Trivial points on towers of curves},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {25},
     number = {2},
     year = {2013},
     pages = {477-498},
     doi = {10.5802/jtnb.845},
     mrnumber = {3228317},
     zbl = {1294.11109},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2013__25_2_477_0}
}
Xarles, Xavier. Trivial points on towers of curves. Journal de théorie des nombres de Bordeaux, Volume 25 (2013) no. 2, pp. 477-498. doi : 10.5802/jtnb.845. http://www.numdam.org/item/JTNB_2013__25_2_477_0/

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