Maximal monodromy in unequal characteristic

Pierre Chrétien (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 fraction field $K$. We study stable models of $p$-cyclic covers of $\Proj_K$. First, we determine the monodromy extension, the monodromy group, its filtration and the Swan conductor for special covers of arbitrarily high genus with potential good reduction. In the case $p=2$ we consider hyperelliptic curves of genus $2$.

Domaines: Géométrie algébrique [math.AG]

Pierre Chrétien, Michel Matignon. Maximal monodromy in unequal characteristic. 2011. ⟨hal-00630159⟩