On the Gille theorem for the relative projective line

Ivan Panin; Anastasia Stavrova

On the Gille theorem for the relative projective line

Algebraic Geometry 2025-01-10 v3

Authors: Ivan Panin , Anastasia Stavrova

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.

Keywords

algebraic varieties projective varieties

Cite

@article{arxiv.2305.16627,
  title  = {On the Gille theorem for the relative projective line},
  author = {Ivan Panin and Anastasia Stavrova},
  journal= {arXiv preprint arXiv:2305.16627},
  year   = {2025}
}

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