---
_id: '12427'
abstract:
- lang: eng
  text: '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.'
article_processing_charge: No
article_type: original
author:
- first_name: Francesca
  full_name: Balestrieri, Francesca
  id: 3ACCD756-F248-11E8-B48F-1D18A9856A87
  last_name: Balestrieri
citation:
  ama: Balestrieri F. Some remarks on strong approximation and applications to homogeneous
    spaces of linear algebraic groups. <i>Proceedings of the American Mathematical
    Society</i>. 2023;151(3):907-914. doi:<a href="https://doi.org/10.1090/proc/15239">10.1090/proc/15239</a>
  apa: Balestrieri, F. (2023). Some remarks on strong approximation and applications
    to homogeneous spaces of linear algebraic groups. <i>Proceedings of the American
    Mathematical Society</i>. American Mathematical Society. <a href="https://doi.org/10.1090/proc/15239">https://doi.org/10.1090/proc/15239</a>
  chicago: Balestrieri, Francesca. “Some Remarks on Strong Approximation and Applications
    to Homogeneous Spaces of Linear Algebraic Groups.” <i>Proceedings of the American
    Mathematical Society</i>. American Mathematical Society, 2023. <a href="https://doi.org/10.1090/proc/15239">https://doi.org/10.1090/proc/15239</a>.
  ieee: F. Balestrieri, “Some remarks on strong approximation and applications to
    homogeneous spaces of linear algebraic groups,” <i>Proceedings of the American
    Mathematical Society</i>, vol. 151, no. 3. American Mathematical Society, pp.
    907–914, 2023.
  ista: Balestrieri F. 2023. Some remarks on strong approximation and applications
    to homogeneous spaces of linear algebraic groups. Proceedings of the American
    Mathematical Society. 151(3), 907–914.
  mla: Balestrieri, Francesca. “Some Remarks on Strong Approximation and Applications
    to Homogeneous Spaces of Linear Algebraic Groups.” <i>Proceedings of the American
    Mathematical Society</i>, vol. 151, no. 3, American Mathematical Society, 2023,
    pp. 907–14, doi:<a href="https://doi.org/10.1090/proc/15239">10.1090/proc/15239</a>.
  short: F. Balestrieri, Proceedings of the American Mathematical Society 151 (2023)
    907–914.
corr_author: '1'
date_created: 2023-01-29T23:00:58Z
date_published: 2023-01-01T00:00:00Z
date_updated: 2024-10-09T21:04:07Z
day: '01'
department:
- _id: TiBr
doi: 10.1090/proc/15239
external_id:
  isi:
  - '000898440000001'
intvolume: '       151'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://hal.science/hal-03013498/
month: '01'
oa: 1
oa_version: Preprint
page: 907-914
publication: Proceedings of the American Mathematical Society
publication_identifier:
  eissn:
  - 1088-6826
  issn:
  - 0002-9939
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Some remarks on strong approximation and applications to homogeneous spaces
  of linear algebraic groups
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 151
year: '2023'
...