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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2019
- DOI:
- 10.48550/arXiv.1910.14251
- arXiv:
- arXiv:1910.14251
- Bibcode:
- 2019arXiv191014251A
- Keywords:
-
- Mathematics - Algebraic Geometry;
- Mathematics - Number Theory;
- 14H40;
- 14H55;
- 11L05
- E-Print:
- 36 pages