{"citation":{"ista":"Browning TD, Boudec PL, Sawin W. 2023. The Hasse principle for random Fano hypersurfaces. Annals of Mathematics. 197(3), 1115–1203.","chicago":"Browning, Timothy D, Pierre Le Boudec, and Will Sawin. “The Hasse Principle for Random Fano Hypersurfaces.” <i>Annals of Mathematics</i>. Princeton University, 2023. <a href=\"https://doi.org/10.4007/annals.2023.197.3.3\">https://doi.org/10.4007/annals.2023.197.3.3</a>.","apa":"Browning, T. D., Boudec, P. L., &#38; Sawin, W. (2023). The Hasse principle for random Fano hypersurfaces. <i>Annals of Mathematics</i>. Princeton University. <a href=\"https://doi.org/10.4007/annals.2023.197.3.3\">https://doi.org/10.4007/annals.2023.197.3.3</a>","ama":"Browning TD, Boudec PL, Sawin W. The Hasse principle for random Fano hypersurfaces. <i>Annals of Mathematics</i>. 2023;197(3):1115-1203. doi:<a href=\"https://doi.org/10.4007/annals.2023.197.3.3\">10.4007/annals.2023.197.3.3</a>","short":"T.D. Browning, P.L. Boudec, W. Sawin, Annals of Mathematics 197 (2023) 1115–1203.","mla":"Browning, Timothy D., et al. “The Hasse Principle for Random Fano Hypersurfaces.” <i>Annals of Mathematics</i>, vol. 197, no. 3, Princeton University, 2023, pp. 1115–203, doi:<a href=\"https://doi.org/10.4007/annals.2023.197.3.3\">10.4007/annals.2023.197.3.3</a>.","ieee":"T. D. Browning, P. L. Boudec, and W. Sawin, “The Hasse principle for random Fano hypersurfaces,” <i>Annals of Mathematics</i>, vol. 197, no. 3. Princeton University, pp. 1115–1203, 2023."},"article_type":"original","language":[{"iso":"eng"}],"_id":"8682","doi":"10.4007/annals.2023.197.3.3","page":"1115-1203","publication":"Annals of Mathematics","author":[{"orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","first_name":"Timothy D"},{"full_name":"Boudec, Pierre Le","first_name":"Pierre Le","last_name":"Boudec"},{"first_name":"Will","last_name":"Sawin","full_name":"Sawin, Will"}],"external_id":{"isi":["000966611000003"],"arxiv":["2006.02356"]},"publication_identifier":{"issn":["0003-486X"]},"isi":1,"intvolume":"       197","volume":197,"year":"2023","publication_status":"published","date_published":"2023-05-01T00:00:00Z","issue":"3","department":[{"_id":"TiBr"}],"abstract":[{"text":"It is known that the Brauer--Manin obstruction to the Hasse principle is vacuous for smooth Fano hypersurfaces of dimension at least 3 over any number field. Moreover, for such varieties it follows from a general conjecture of Colliot-Thélène that the Brauer--Manin obstruction to the Hasse principle should be the only one, so that the Hasse principle is expected to hold. Working over the field of rational numbers and ordering Fano hypersurfaces of fixed degree and dimension by height, we prove that almost every such hypersurface satisfies the Hasse principle provided that the dimension is at least 3. This proves a conjecture of Poonen and Voloch in every case except for cubic surfaces.","lang":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/2006.02356","open_access":"1"}],"type":"journal_article","day":"01","month":"05","article_processing_charge":"No","date_updated":"2023-10-17T12:47:43Z","quality_controlled":"1","title":"The Hasse principle for random Fano hypersurfaces","related_material":{"link":[{"url":"https://ist.ac.at/en/news/when-is-necessary-sufficient/","description":"News on IST Homepage","relation":"press_release"}]},"status":"public","oa":1,"oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2020-10-19T14:28:50Z","publisher":"Princeton University"}