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

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

2002-03-25

arxiv.org/abs/math/0203259v1

Mathematics

Number Theory

36 pages, to appear in journal of Number Theory

Scientific paper

Let 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 $k[[t]]$.

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