Fp-espaces vectoriels de formes differérentielles logarithmiques sur la droite projective

Abstract

Let k be an algebraically closed field of characteristic p > 0. Let m ε ∌, (m, p) = 1. We study p-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 (ℤ/pℤ)n actions as k-automorphisms of k[[t]]. © 2002 Elsevier Science (USA).