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

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 r(x) 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 r(x) and to prove Kato's conjecture Kato (1994) [1] for an upper bound of r(x) for a good Artin-Schreier extension. (C) 2014 Elsevier Inc. All rights reserved.