{"abstract":[{"lang":"eng","text":"Châtelet surfaces provide a rich source of geometrically rational surfaces that do not always satisfy the Hasse principle. Restricting attention to a special class of Châtelet surfaces, we investigate the frequency that such counter-examples arise over the rational numbers."}],"status":"public","date_created":"2018-12-11T11:45:26Z","intvolume":"       108","publication":"Proceedings of the London Mathematical Society","date_updated":"2021-01-12T06:57:51Z","quality_controlled":0,"date_published":"2013-11-29T00:00:00Z","year":"2013","day":"29","author":[{"full_name":"de la Bretèche, Régis","first_name":"Régis","last_name":"De La Bretèche"},{"full_name":"Timothy Browning","first_name":"Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning"}],"publist_id":"7652","extern":1,"acknowledgement":"While working on this paper, the first author was supported by an IUF Junior and ANR while the second author was supported by ERC grant 306457.","main_file_link":[{"url":"https://arxiv.org/abs/1210.4010","open_access":"1"}],"page":"1030 - 1078","publisher":"Oxford University Press","oa":1,"publication_status":"published","volume":108,"month":"11","title":"Density of Châtelet surfaces failing the Hasse principle","issue":"4","_id":"250","doi":"10.1112/plms/pdt060","type":"journal_article","citation":{"ama":"De La Bretèche R, Browning TD. Density of Châtelet surfaces failing the Hasse principle. <i>Proceedings of the London Mathematical Society</i>. 2013;108(4):1030-1078. doi:<a href=\"https://doi.org/10.1112/plms/pdt060\">10.1112/plms/pdt060</a>","ista":"De La Bretèche R, Browning TD. 2013. Density of Châtelet surfaces failing the Hasse principle. Proceedings of the London Mathematical Society. 108(4), 1030–1078.","chicago":"De La Bretèche, Régis, and Timothy D Browning. “Density of Châtelet Surfaces Failing the Hasse Principle.” <i>Proceedings of the London Mathematical Society</i>. Oxford University Press, 2013. <a href=\"https://doi.org/10.1112/plms/pdt060\">https://doi.org/10.1112/plms/pdt060</a>.","ieee":"R. De La Bretèche and T. D. Browning, “Density of Châtelet surfaces failing the Hasse principle,” <i>Proceedings of the London Mathematical Society</i>, vol. 108, no. 4. Oxford University Press, pp. 1030–1078, 2013.","mla":"De La Bretèche, Régis, and Timothy D. Browning. “Density of Châtelet Surfaces Failing the Hasse Principle.” <i>Proceedings of the London Mathematical Society</i>, vol. 108, no. 4, Oxford University Press, 2013, pp. 1030–78, doi:<a href=\"https://doi.org/10.1112/plms/pdt060\">10.1112/plms/pdt060</a>.","short":"R. De La Bretèche, T.D. Browning, Proceedings of the London Mathematical Society 108 (2013) 1030–1078.","apa":"De La Bretèche, R., &#38; Browning, T. D. (2013). Density of Châtelet surfaces failing the Hasse principle. <i>Proceedings of the London Mathematical Society</i>. Oxford University Press. <a href=\"https://doi.org/10.1112/plms/pdt060\">https://doi.org/10.1112/plms/pdt060</a>"}}