Torsion points on Fermat quotients of the form $y^n = x^d + 1$

Vishal Arul

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arXiv · 1910.14251

Torsion points on Fermat quotients of the form $y^n = x^d + 1$

Vishal Arul

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Abstract

We classify all geometric torsion points on the Fermat quotients $y^n = x^d + 1$ where $n, d \ge 2$ are coprime. In addition, we classify all geometric torsion points on the generic superelliptic curve $y^n = (x - a_1) \cdots (x - a_d)$, extending a result of Poonen and Stoll, who considered the hyperelliptic $n = 2$ case.

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Vishal Arul. 2020-05-03. Torsion points on Fermat quotients of the form $y^n = x^d + 1$. https://arxiv.org/abs/1910.14251

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