$F_p$-espaces vectoriels de formes différentielles logarithmiques sur la droite projective

Abstract

Let k be an algebraically closed field of characteristic p >0. Let $m\in \mathbb{N}$, (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 $(\mathbb{Z}/p\mathbb{Z}{)}^n$ actions as k-automorphisms of $k[[t]]$.

36 pages, to appear in journal of Number Theory