Residue Free Differentials and the Cartier Operator for Algebraic Function Fields of one Variable

Source abstract

Let K be a field of characteristic p > 0 and let A be a separably generated algebraic function field of one variable with K as its exact constant field. Throughout this paper we shall use the following notations to classify differentials of A/K: D(A) : the K-module of all differentials, G(A) : the K-module of all differentials of the first kind, R(A) : the K-module of all residue free differentials in the sense of Chevalley [ 2 , p. 48], E * (A) : the K-module of all pseudo-exact differentials in the sense of Lamprecht [ 7 , p. 363], (compare the definition with our Lemma 8).