Local-global principles for constant reductive groups over semi-global fields
Algebraic Geometry
2023-07-12 v2
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.
Cite
@article{arxiv.2108.12349,
title = {Local-global principles for constant reductive groups over semi-global fields},
author = {Jean-Louis Colliot-Thélène and David Harbater and Julia Hartmann and Daniel Krashen and R. Parimala and V. Suresh},
journal= {arXiv preprint arXiv:2108.12349},
year = {2023}
}
Comments
59 pages. Some improved phrasing to clarify the presentation