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arXiv · 2108.12349

Local-global principles for constant reductive groups over semi-global fields

Jean-Louis Colliot-Thélène·David Harbater·Julia Hartmann·Daniel Krashen·R. Parimala·V. Suresh
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Abstract

We study local-global principles for torsors under reductive linear algebraic groups over semi-global fields; i.e., over one variable function fields over complete discretely valued fields. We provide conditions on the group and the semiglobal field under which the local-global principle holds, and we compute the obstruction to the local-global principle in certain classes of examples. Using our description of the obstruction, we give the first example of a semisimple simply connected group over a semi-global field where the local-global principle fails. Our methods include patching and R-equivalence.

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Jean-Louis Colliot-Thélène, David Harbater, Julia Hartmann, Daniel Krashen, R. Parimala, V. Suresh. 2021-08-27. Local-global principles for constant reductive groups over semi-global fields. https://arxiv.org/abs/2108.12349

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