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MODELS OF TORSORS OVER AFFINE SPACES

Part of: Arithmetic algebraic geometry Algebraic groups

Published online by Cambridge University Press:  07 March 2019

Marco Antei  and
Jorge Esquivel Araya
Marco Antei
Affiliation:
Escuela de Matematica, Universidad de Costa Rica, Ciudad universitaria Rodrigo Facio Brenes, Costa Rica email marco.antei@ucr.ac.cr
Jorge Esquivel Araya
Affiliation:
Escuela de Matematica, Universidad de Costa Rica, Ciudad universitaria Rodrigo Facio Brenes, Costa Rica email jorge.esquivelaraya@ucr.ac.cr
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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.

MSC classification

Primary: 14L30: Group actions on varieties or schemes (quotients) 14L15: Group schemes
Secondary: 11G99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 65 , Issue 3 , 2019 , pp. 530 - 541
Copyright
Copyright © University College London 2019 

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