On torsion of superelliptic Jacobians. (English. French summary) Zbl 1475.14054
Summary: We prove a result describing the structure of a specific subgroup of the \(m\)-torsion of the Jacobian of a general superelliptic curve \(y^m=F(x)\), generalizing the structure theorem for the \(2\)-torsion of a hyperelliptic curve. 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 \(\mathbb{Q}\).
MSC:
| 14H40 | Jacobians, Prym varieties |
| 14G10 | Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) |
| 14H45 | Special algebraic curves and curves of low genus |
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