On ramifications of Artin–Schreier extensions of surfaces over algebraically closed fields of positive characteristic II

Abstract

For a smooth surface X over an algebraically closed field of positive characteristic, we consider the ramification of an Artin–Schreier extension of X. A ramification at a point of codimension 1 of X is understood by the Swan conductor. A ramification at a closed point of X is understood by the invariant rx defined by Kato (1994) [1]. The main theme of this paper is to construct the Young diagram Y(X, D, x) which is closely related to rx and to prove Kato's conjecture Kato (1994) [1] for an upper bound of rx for a good Artin–Schreier extension.