Stable (and good) reduction of three point covers
Abstract
If f: Y --> X is a three-point G-Galois cover of the
projective line over a p-adic field, then it has good reduction
when |G| is prime to p. When p divides
|G|, the cover may no longer have good reduction, but there
is at least a stable model. We prove some properties of the stable
model of f when |G| has a cyclic p-Sylow group.
When f is defined over a "small" field, we show that it is
impossible for these properties to be satisfied, and thus that f
must have good reduction.