Raynaud's group-scheme and reduction of coverings

Abstract

The structure of the reduction of an admissible $G$-covering $Y \to X$ at primes $p$ dividing $|G|$ is investigated. Assume $|G|$ is not divisible by $p^2$ and the $p$-Sylow group is normal. Following Raynaud it is shown that there is a group scheme $\cG$ over the smooth locus of $X$ for which $Y$ is still a principal bundle away from the special points. A structure at the nodes involving Artin twisted curves is discussed.