Jacobian decomposition conjecture for elementary abelian actions

Let $p\geqslant 2$ be a prime number and let $(S,N)$ be a $\mathbb{Z}_p^m$-action of signature $(0;p^{n+1})$, where $2\leqslant m\leqslant n-1$. For each subgroup $L\leqslant N$ with $L\cong\mathbb{Z}_p^{m-1}$, let $S_L$ denote the underlying Riemann surface of the orbifold quotient $S/L$. Jacobian decomposition conjecture. The Jacobian variety of $S$ is isogenous to the product of the Jacobian varieties of these quotient surfaces:

$$JS\sim\prod_{L\in\mathscr{L}}JS_L,\qquad \mathscr{L}=\{L\leqslant N:L\cong\mathbb{Z}_p^{m-1}\}.$$

This conjecture proposes an isogeny decomposition of the Jacobian associated with a $\mathbb{Z}_p^m$-action, extending the decomposition obtained from generalized Fermat pairs and the relation between the Jacobians of a covering surface and its quotient. The supplied text does not indicate whether the conjecture has been proved or disproved.