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MODELS OF TORSORS OVER AFFINE SPACES

Published online by Cambridge University Press:  07 March 2019

Marco Antei
Affiliation:
Escuela de Matematica, Universidad de Costa Rica, Ciudad universitaria Rodrigo Facio Brenes, Costa Rica email [email protected]
Jorge Esquivel Araya
Affiliation:
Escuela de Matematica, Universidad de Costa Rica, Ciudad universitaria Rodrigo Facio Brenes, Costa Rica email [email protected]
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Abstract

Let $X:=\mathbb{A}_{R}^{n}$ be the $n$-dimensional affine space over a discrete valuation ring $R$ with fraction field $K$. We prove that any pointed torsor $Y$ over $\mathbb{A}_{K}^{n}$ under the action of an affine finite-type group scheme can be extended to a torsor over $\mathbb{A}_{R}^{n}$ possibly after pulling $Y$ back over an automorphism of $\mathbb{A}_{K}^{n}$. The proof is effective. Other cases, including $X=\unicode[STIX]{x1D6FC}_{p,R}$, are also discussed.

Type
Research Article
Copyright
Copyright © University College London 2019 

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