English

On the existence of a torsor structure for Galois covers

Algebraic Geometry 2007-05-23 v1

Abstract

Let RR be a complete discrete valuation ring with residue characteristic p>0p>0. In this note we give an example of a Galois cover f:YXf:Y\to X between flat and normal formal RR-schemes of finite type which is \'etale above the generic fibre of XX such that the special fibre of YY is reduced and such that ff doesn't have the structure of a torsor under a finite and flat RR group scheme. In the example RR has equal characteristic pp and the Galois group of the cover is cyclic of order p2p^2. In the example the formal scheme XX is affine and can be choosen to be even smooth.

Keywords

Cite

@article{arxiv.math/0403389,
  title  = {On the existence of a torsor structure for Galois covers},
  author = {Saidi Mohamed},
  journal= {arXiv preprint arXiv:math/0403389},
  year   = {2007}
}

Comments

These notes are not intended for publication