{"oa_version":"Preprint","oa":1,"date_created":"2023-01-29T23:00:58Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"American Mathematical Society","scopus_import":"1","title":"Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups","quality_controlled":"1","status":"public","type":"journal_article","day":"01","article_processing_charge":"No","month":"01","date_updated":"2023-08-01T13:03:32Z","date_published":"2023-01-01T00:00:00Z","publication_status":"published","issue":"3","department":[{"_id":"TiBr"}],"main_file_link":[{"url":"https://hal.science/hal-03013498/","open_access":"1"}],"abstract":[{"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.","lang":"eng"}],"intvolume":"       151","volume":151,"year":"2023","isi":1,"author":[{"full_name":"Balestrieri, Francesca","id":"3ACCD756-F248-11E8-B48F-1D18A9856A87","first_name":"Francesca","last_name":"Balestrieri"}],"publication":"Proceedings of the American Mathematical Society","page":"907-914","doi":"10.1090/proc/15239","external_id":{"isi":["000898440000001"]},"publication_identifier":{"eissn":["1088-6826"],"issn":["0002-9939"]},"article_type":"original","citation":{"short":"F. Balestrieri, Proceedings of the American Mathematical Society 151 (2023) 907–914.","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>","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.","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.","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>."},"_id":"12427","language":[{"iso":"eng"}]}