@article{12427,
  abstract     = {Let k be a number field and X a smooth, geometrically integral quasi-projective variety over k. For any linear algebraic group G over k and any G-torsor g : Z → X, we observe that if the étale-Brauer obstruction is the only one for strong approximation off a finite set of places S for all twists of Z by elements in H^1(k, G), then the étale-Brauer obstruction is the only one for strong approximation off a finite set of places S for X. As an application, we show that any homogeneous space of the form G/H with G a connected linear algebraic group over k satisfies strong approximation off the infinite places with étale-Brauer obstruction, under some compactness assumptions when k is totally real. We also prove more refined strong approximation results for homogeneous spaces of the form G/H with G semisimple simply connected and H finite, using the theory of torsors and descent.},
  author       = {Balestrieri, Francesca},
  issn         = {1088-6826},
  journal      = {Proceedings of the American Mathematical Society},
  number       = {3},
  pages        = {907--914},
  publisher    = {American Mathematical Society},
  title        = {{Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups}},
  doi          = {10.1090/proc/15239},
  volume       = {151},
  year         = {2023},
}