Raynaud's group-scheme and reduction of coverings

Dan Abramovich; Jonathan Lubin

Raynaud's group-scheme and reduction of coverings

Algebraic Geometry 2009-03-10 v2

Authors: Dan Abramovich , Jonathan Lubin

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.

Keywords

raynaud group scheme g-coverings reduction admissible covering principal bundle artin twisted curves

Cite

@article{arxiv.math/0304352,
  title  = {Raynaud's group-scheme and reduction of coverings},
  author = {Dan Abramovich and Jonathan Lubin},
  journal= {arXiv preprint arXiv:math/0304352},
  year   = {2009}
}

Comments

Results much improved thanks to computations of Romagny, hopefully leading to complete moduli space in joint work in the near future. Added appendix by Lubin, of which this is the fun version. If you want to see the master working in Lubin Tate theory read this - the published version, he threatens, will be cut and dry

Raynaud's group-scheme and reduction of coverings

Abstract

Keywords

Cite

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