Raynaud's group-scheme and reduction of coverings

Details Raynaud's group-scheme and reduction of coverings Raynaud's group-scheme and reduction of coverings

2003-04-23

arxiv.org/abs/math/0304352v2

Mathematics

Algebraic Geometry

Results much improved thanks to computations of Romagny, hopefully leading to complete moduli space in joint work in the near

Scientific paper

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.

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