Galois Covers of Degree <em>p</em> and Semi-Stable Reduction of Curves in Mixed Characteristics

Abstract

In this paper we study the degeneration of a Galois cover f : Y → X of degree p above a proper and smooth curve X over a complete discrete valuation ring of mixed characteristics (0, p). We exhibit geometric and combinatorial degeneration data which describe the geometry of the special fiber of a minimal semi-stable model of Y.