On the existence of a torsor structure for Galois covers

2004/03/23 by Saidi Mohamed, Mohamed, Saidi
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0403389

These notes are not intended for publication

arxiv created 2004/03/23 · arxiv updated 2009/12/01

Abstract

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→ X between flat and normal formal R-schemes of finite type which is étale 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 p². In the example the formal scheme X is affine and can be choosen to be even smooth.

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