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

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.

36 pages; improved exposition, reorganized sections to separate geometry and arithmetic and to avoid faulty Lemma 2.12 of v1, redid Magma calculations to work over finite fields instead over C to avoid interval arithmetic