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David Grant; Delphy Shaulis
The cuspidal torsion packet on hyperelliptic Fermat quotients
Journal de théorie des nombres de Bordeaux, 16 no. 3 (2004), p. 577-585, doi: 10.5802/jtnb.462
Article PDF | Reviews MR 2144959 | Zbl 1069.11024

Résumé - Abstract

Let $\ell \ge 7$ be a prime, $C$ be the non-singular projective curve defined over $\mathbb{Q}$ by the affine model $y(1-y)=x^\ell $, $\infty $ the point of $C$ at infinity on this model, $J$ the Jacobian of $C$, and $\phi : C\rightarrow J$ the albanese embedding with $\infty $ as base point. Let $\overline{\mathbb{Q}}$ be an algebraic closure of $\mathbb{Q}$. Taking care of a case not covered in [12], we show that $\phi (C)\cap J_{\operatorname{tors}}(\overline{\mathbb{Q}})$ consists only of the image under $\phi $ of the Weierstrass points of $C$ and the points $(x,y)=(0,0)$ and $(0,1)$, where $J_{\operatorname{tors}}$ denotes the torsion points of $J$.

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