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Quadratic torsion orders on Jacobian varieties (2410.14455v1)
Published 18 Oct 2024 in math.NT and math.AG
Abstract: We establish the existence of hyperelliptic curves of genus $g\ge 2$ defined over $\mathbb{Q}$ whose Jacobians possess rational torsion points of order $N$ where $N=4g2+2g-2$ or $4g2+ 2g -4$. For $N=2g2+7g+1$, we introduce a $1$-parameter family of hyperelliptic curves of genus $g$ over $\mathbb{Q}$ with a rational torsion point of order $N$ on their Jacobians.