On the existence of a torsor structure for Galois covers

Details On the existence of a torsor structure for Galois covers On the existence of a torsor structure for Galois covers

2004-03-23

arxiv.org/abs/math/0403389v1

Mathematics

Algebraic Geometry

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Scientific paper

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

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