The cuspidal torsion packet on hyperelliptic Fermat quotients
Journal de théorie des nombres de Bordeaux, Volume 16 (2004) no. 3, p. 577-585

Let 7 be a prime, C be the non-singular projective curve defined over by the affine model y(1-y)=x , the point of C at infinity on this model, J the Jacobian of C, and φ:CJ the albanese embedding with as base point. Let ¯ be an algebraic closure of . Taking care of a case not covered in [12], we show that φ(C)J tors ( ¯) consists only of the image under φ of the Weierstrass points of C and the points (x,y)=(0,0) and (0,1), where J tors denotes the torsion points of J.

Soit 7 un nombre premier, soit C la courbe projective lisse définie sur par le modèle affine y(1-y)=x , soit le point à l’infini de ce modèle de C, soit J la jacobienne de C et soit φ:CJ le morphisme d’Abel-Jacobi associé à . Soit ¯ une clôture algébrique de . Nous traitons ici un cas non couvert dans [12], en montrant que φ(C)J tors ( ¯) est composé de l’image par φ des points de Weierstrass de C ainsi que les points (x,y)=(0,0) et (0,1) de C. Ici, J tors désigne les points de torsion de J.

@article{JTNB_2004__16_3_577_0,
     author = {Grant, David and Shaulis, Delphy},
     title = {The cuspidal torsion packet on hyperelliptic Fermat quotients},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux 1},
     volume = {16},
     number = {3},
     year = {2004},
     pages = {577-585},
     doi = {10.5802/jtnb.462},
     mrnumber = {2144959},
     zbl = {1069.11024},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2004__16_3_577_0}
}
Grant, David; Shaulis, Delphy. The cuspidal torsion packet on hyperelliptic Fermat quotients. Journal de théorie des nombres de Bordeaux, Volume 16 (2004) no. 3, pp. 577-585. doi : 10.5802/jtnb.462. http://www.numdam.org/item/JTNB_2004__16_3_577_0/

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