On torsion of superelliptic Jacobians
Journal de Théorie des Nombres de Bordeaux, Tome 33 (2021) no. 1, pp. 223-235.

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 .

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 .

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DOI : https://doi.org/10.5802/jtnb.1158
Classification : 14H40,  14G10,  14H45
Mots clés : Jacobian variety, superelliptic curves, Mordell–Weil group
@article{JTNB_2021__33_1_223_0,
     author = {Wojciech Wawr\'ow},
     title = {On torsion of superelliptic {Jacobians}},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {223--235},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {33},
     number = {1},
     year = {2021},
     doi = {10.5802/jtnb.1158},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1158/}
}
Wojciech Wawrów. On torsion of superelliptic Jacobians. Journal de Théorie des Nombres de Bordeaux, Tome 33 (2021) no. 1, pp. 223-235. doi : 10.5802/jtnb.1158. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1158/

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