On torsion of superelliptic Jacobians
Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 1, pp. 223-235.

We prove a result describing the structure of a specific subgroup of the m-torsion of the Jacobian of a general superelliptic curve y m =F(x), generalizing the structure theorem for the 2-torsion of a hyperelliptic curve. We study existence of torsion on curves of the form y q =x p -x+a over finite fields of characteristic p. We apply those results to bound from below the Mordell–Weil ranks of Jacobians of certain superelliptic curves over .

Nous démontrons un résultat décrivant la structure d’un sous- groupe de m-torsion spécifique de la jacobienne d’une courbe superelliptique générale de la forme y m =F(x), généralisant ainsi le théorème de structure pour la 2-torsion d’une courbe hyperelliptique. Nous étudions l’existence de points de torsion sur les courbes de la forme y q =x p -x+a sur les corps finis de caractéristique p. Nous appliquons ces résultats à la minoration du rank de Mordell–Weil des jacobiennes de certaines courbes superelliptiques sur .

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1158
Classification: 14H40, 14G10, 14H45
Keywords: Jacobian variety, superelliptic curves, Mordell–Weil group
Wawrów, Wojciech 1

1 Adam Mickiewicz University Faculty of Mathematics and Computer Science Uniwersytetu Poznańskiego 4 61-614 Poznań, Poland
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Wawrów, Wojciech. On torsion of superelliptic Jacobians. Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 1, pp. 223-235. doi : 10.5802/jtnb.1158. http://archive.numdam.org/articles/10.5802/jtnb.1158/

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