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On the Gille theorem for the relative projective line

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arxiv 2305.16627 v3 pith:7QOHVIIL submitted 2023-05-26 math.AG

Ivan Panin , Anastasia Stavrova This is my paper · ORCID
classification math.AG
keywords locallyschemetrivialzariskibundlegillegroupinfty
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Generically trivial torsors under constant groups

    math.AG 2025-05 conditional novelty 8.0 of 10

    Every generically trivial torsor under a smooth group scheme over a smooth variety over any field is Zariski semilocally trivial, settling the Grothendieck-Serre question.

  2. Constant case of the Grothendieck-Serre conjecture in mixed characteristic

    math.AG 2024-12 conditional novelty 8.0 of 10

    The constant case of the Grothendieck-Serre conjecture is proved for reductive group schemes over any geometrically regular local algebra over a mixed-characteristic DVR.

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