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A principal $G$-bundle, where $G$ denotes any topological group, is a fiber bundle $\pi :P → X$ together with a continuous right action $P × G → P$ such that $G$ preserves the fibers of $P$ and acts freely and transitively on them.

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Extending $G$-torsors on open subsets of affine space

Let $k$ be a characteristic zero field, $V \subset \mathbb{A}^n_k$ an open subscheme, $G$ a split reductive group over $k$ and $T$ a $G$-torsor over $V$ (in the etale, equivalently fppf topology). Sup …
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2 votes
Accepted

Extending $G$-torsors on open subsets of affine space

In case this might be useful to anyone, it turns out that results of Colliot--Thelene can be used to resolve a closely related question: see Theorem 6.1 in the following preprint (apologies for the se …
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