On the Gille theorem for the relative projective line

Ivan Panin; Anastasia Stavrova

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arXiv · 2305.16627

On the Gille theorem for the relative projective line

Ivan Panin·Anastasia Stavrova

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Abstract

Let $X$ be a Noetherian separated scheme. Let $G$ be a reductive $X$-group scheme, and let $E$ be a principal $G$-bundle over $\mathbb{P}^1_X$. We prove that if the restriction of $E$ to $\infty\times X$ is Zariski locally trivial, then $E$ is itself Zariski locally trivial.

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Ivan Panin, Anastasia Stavrova. 2023-05-26. On the Gille theorem for the relative projective line. https://arxiv.org/abs/2305.16627

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