Exponents of Jacobians and relative class groups

Borys Kadets, Daniel Keliher

We prove a lower bound for the exponent of the relative class group ${\mathrm{Pic}}^0{X}_1/{\varphi }^{\ast }{\mathrm{Pic}}^0{X}_2$ for a covering of curves $X_1\to X_2$ over a finite field $\mathbb{…