Mathematical Research Letters

Volume 24 (2017)

Number 1

Weak approximation for homogeneous spaces: reduction to the case with finite stabilizer

Pages: 1 – 19



Giancarlo Lucchini Arteche (Centre de Mathématiques Laurent Schwartz, École polytechnique, Palaiseau, France)


We reduce the question about whether the Brauer–Manin obstruction to weak approximation for homogeneous spaces is the only obstruction to the “simpler” question of the particular case of homogeneous spaces of $\mathrm{SL}_n$ with finite stabilizer. We also give unconditional results based on the few known results on finite stabilizers.


homogeneous spaces, weak approximation, Brauer–Manin obstruction

2010 Mathematics Subject Classification

14G05, 14M17

Received 23 July 2015

Accepted 9 January 2016

Published 7 June 2017