2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63652Let k be an algebraically closed field of characteristic p >0. Let $m \in \N$, (m,p)=1. We study $\fp$-vector spaces of logarithmic differential forms on the projective line such that each non zero form has a unique zero at $\infty$ of given order m-1. We discuss the existence of such vectors spaces according to the value of m. We give applications to the lifting to characteristic 0 of $(\Z /p\Z)^n$ actions as k-automorphisms of $k[[t]]$.36 pages, to appear in journal of Number TheoryNumber TheoryAlgebraic Geometry14D15; 14E22; 14F10; 14L30text