Branched covers of $\mathbb{P}^1$ and divisibility in class group

TL;DR

The paper explores how torsion points on Jacobians of m-gonal curves can generate torsion elements in the class groups of specific number fields, linking algebraic geometry with number theory.

Contribution

It introduces a method to produce class group torsion elements from Jacobian torsion points on m-gonal curves, connecting geometric and arithmetic properties.

Findings

Constructs new torsion elements in class groups from Jacobian torsion points.

Establishes a link between algebraic geometry of curves and number field class groups.

Abstract

We start with $n$-torsions in the Jacobian of an $m$-gonal curve and produce $n$-torsions in the class group of certain number field $K$.