Mathematical Research Letters

Volume 24 (2017)

Number 1

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

Pages: 1 – 19

DOI: http://dx.doi.org/10.4310/MRL.2017.v24.n1.a1

Author

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

Abstract

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.

Keywords

homogeneous spaces, weak approximation, Brauer–Manin obstruction

2010 Mathematics Subject Classification

14G05, 14M17

Full Text (PDF format)

Paper received on 23 July 2015.