article published yes Francesca Balestrieri author 3ACCD756-F248-11E8-B48F-1D18A9856A87 TiBr department 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. American Mathematical Society2023 eng 0002-9939 1088-6826 00089844000000110.1090/proc/15239 1513907-914 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. 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>. 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. 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>. 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> 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> F. Balestrieri, Proceedings of the American Mathematical Society 151 (2023) 907–914. 124272023-01-29T23:00:58Z2026-07-29T10:09:11Z