2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121589Let $k_{\infty}$ be a $\Z_p^d$-extension of a global function field $k$ of characteristic $p$. Let $\Cl_{k_{\infty},p}$ be the $p$ completion of the class group of $k_{\infty}$. We prove that the characteristic ideal of the Galois module $\Cl_{k_{\infty},p}$ is generated by the Stickelberger element of Gross which calculates the special values of $L$ functions.26 pagesNumber Theory11S40 (primary), 11R42, 11R58 (secondary)text