2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71349In this paper we study the semi-stable reduction of $p$ and $p^2$-cyclic covers of curves in equal characteristic $p>0$. The main tool we use is the classical Artin-Schreier-Witt theory for $p^n$-cyclic covers in characteristic $p$. Although the results of this paper concern only the cases of degree $p$ and $p^2$-cyclic cover we develop the techniques and the framework in which the general cyclic case can be studied.54 pagesAlgebraic GeometryNumber Theorytext