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

Vishal Arul

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

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arxiv 1910.14251 v2 pith:F4P22E7E submitted 2019-10-31 math.AG math.NT

Vishal Arul This is my paper · ORCID

classification math.AGmath.NT

keywords pointstorsionclassifyfermatgeometricquotientsadditioncase

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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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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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