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

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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.

fields

hep-th 1

years

2025 1

verdicts

CONDITIONAL 1

representative citing papers

On W-algebras and ODE/IM correspondence

hep-th · 2025-08-28 · conditional · novelty 6.0

The eigenvalues of quantum KdV-type charges in Virasoro, W3, and W4 algebras are computed from Bethe roots via WKB periods of Catalan curves, verified against direct CFT diagonalization.

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  • On W-algebras and ODE/IM correspondence hep-th · 2025-08-28 · conditional · none · ref 89 · internal anchor

    The eigenvalues of quantum KdV-type charges in Virasoro, W3, and W4 algebras are computed from Bethe roots via WKB periods of Catalan curves, verified against direct CFT diagonalization.