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arXiv · 1809.06236

Models of torsors over affine spaces

Marco Antei·Jorge A. Esquivel A
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Abstract

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

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Marco Antei, Jorge A. Esquivel A. 2018-09-13. Models of torsors over affine spaces. https://doi.org/10.1112/s0025579319000068

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