Ramification of surfaces: Artin-Schreier extensions

Details Ramification of surfaces: Artin-Schreier extensions Ramification of surfaces: Artin-Schreier extensions

2002-09-15

arxiv.org/abs/math/0209183v1

Contemporary mathematics 300 (2002), 211--220

Mathematics

Algebraic Geometry

LaTeX, 9 pages

Scientific paper

Let $A$ be a regular 2-dimensional local ring of characteristic $p>0$, and let $L/K$ be a cyclic extension of degree $p$ of its field of fractions such that the corresponding branch divisor is normal crossing. For each $\gp\in\Spec A$ of height 1 such that $A/\gp$ is regular, consider the ramification jump $h_\gp$ of the extension of the residue field at $\gp$. In this paper the semi-continuity of $h_\gp$ with respect to Zariski topology of suitable jet spaces is proved. The asymptotic of $h_\gp$ with respect to intersection multiplicity of the prime divisor defined by $\gp$ and the branch divisor is also addressed.

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