Translator Disclaimer
August 2022 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
Michigan Math. J. 72: 77-144 (August 2022). DOI: 10.1307/mmj/20217219

Abstract

We study local-global principles for torsors under reductive linear algebraic groups over semi-global fields; that is, over one-variable function fields over complete discretely valued fields. We provide conditions on the group and the semi-global 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.

Dedication

To Gopal Prasad on his 75th birthday

Citation

Download Citation

Jean-Louis Colliot-Thélène. David Harbater. Julia Hartmann. Daniel Krashen. R. Parimala. V. Suresh. "Local-Global Principles for Constant Reductive Groups over Semi-Global Fields." Michigan Math. J. 72 77 - 144, August 2022. https://doi.org/10.1307/mmj/20217219

Information

Received: 24 August 2021; Revised: 4 January 2022; Published: August 2022
First available in Project Euclid: 2 August 2022

Digital Object Identifier: 10.1307/mmj/20217219

Subjects:
Primary: 11E72 , 12G05 , 14G05
Secondary: 14G27 , 14H25 , 20G15

Rights: Copyright © 2022 The University of Michigan

JOURNAL ARTICLE
68 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.72 • August 2022
Back to Top