Models of torsors over affine spaces

Abstract

Let X := A n R be the n-dimensional affine space over a discrete valuation ring R with fraction field K. We prove that any pointed torsor Y over A n K under the action of an affine finite-type group scheme can be extended to a torsor over A n R possibly after pulling Y back over an automorphism of A n K . The proof is effective. Other cases, including X = αp,R, are also discussed.