ON RESIDUE FREE DIFFERENTIAL FORMS OF AN ALGEBRAIC SCHEME OVER A FIELD OF CHARACTERISTIC p

Let V be an n-dimensional non-singular algebraic integral scheme over a perfect field k of characteristic p > 0 and K its algebraic function field.In this paper, we will prove the following:Let be a differential form in Z (K/k).Then the following three conditions are equivalent:(1) is residue free on V , (2) there exists an integer N such thatThe above theorem is a generalization of the main theorem in Nakakoshi [5].He proved the theorem in case of degree() = n.