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arXiv · 1911.05431

On torsion of superelliptic Jacobians

Wojciech Wawrów
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Abstract

We give a structure theorem for the $m$-torsion of the Jacobian of a general superelliptic curve $y^m=F(x)$. We study existence of torsion on curves of the form $y^q=x^p-x+a$ over finite fields of characteristic $p$. We apply those results to bound from below the Mordell-Weil ranks of Jacobians of certain superelliptic curves over $\mathbb Q$.

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Wojciech Wawrów. 2019-11-13. On torsion of superelliptic Jacobians. https://doi.org/10.5802/jtnb.1158

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