On the Gille theorem for the relative projective line: I

2023/04/19 by Panin, Ivan, Stavrova, Anastasia
#Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2304.09465

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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