Maximal wild monodromy in unequal characteristic

Claus Lehr (1) , Michel Matignon (1)

1 IMB - Institut de Mathématiques de Bordeaux

Let $R$ be a complete discrete valuation ring of mixed characteristic $(0,p)$ with field of fractions $K$ containing the $p$-th roots of unity and $C \la \PK$ a $p$-cyclic cover of the projective line. In this paper we study the finite monodromy extension of the curve $C$, i.e.\ the minimal finite extension $K'/K$ over which $C$ has a stable model. In particular we are interested in the wild part of this extension. In various examples we have shown that the finite monodromy can be maximal, i.e.\ attain certain bounds that were given in previous work by the authors.

Domaines: Géométrie algébrique [math.AG]

Claus Lehr, Michel Matignon. Maximal wild monodromy in unequal characteristic. 2006. ⟨hal-00281800⟩