On the Gille theorem for the relative projective line: I

Ivan Panin; Anastasia Stavrova

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arXiv · 2304.09465

On the Gille theorem for the relative projective line: I

Ivan Panin·Anastasia Stavrova

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Abstract

We prove a relative version of a theorem on torsors on the projective line due to Philippe Gille. As a consequence we obtain a ``weak homotopy invariance'' result for torsors under reductive group schemes defined over arbitrary semi-local regular domains. Specifically, only regular semi-local domains with infinite residue fields are regarded in this preprint. However, all results of the present preprint are true (after minor modifications) for arbitrary semi-local regular domains. This will be the topic of our next preprint.

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Ivan Panin, Anastasia Stavrova. 2023-04-19. On the Gille theorem for the relative projective line: I. https://arxiv.org/abs/2304.09465

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