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arXiv · 1507.00097

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

Masao Oi
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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 r_x defined by Kato [2]. The main theme of this paper is to give a simple formula to compute r_x' defined in [4], which is equal to r_x for good Artin-Schreier extension. We also prove Kato's conjecture for upper bound of r_x.

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Masao Oi. 2015-07-01. On ramifications of Artin-Schreier extensions of surfaces over algebraically closed fields of positive characteristic III. https://arxiv.org/abs/1507.00097

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