imagep-espaces vectoriels de formes différentielles logarithmiques sur la droite projective Original Research Article

Let k be an algebraically closed field of characteristic p>0. Let mset membership, variantimage, (m,p)=1. We study imagep-vector spaces of logarithmic differential forms on the projective line such that each non-zero form has a unique zero at ∞ 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 (image/pimage)n actions as k-automorphisms of k[[t]].