--- _id: '228' abstract: - lang: eng text: Let X be a projective non-singular quartic hypersurface of dimension 39 or more, which is defined over . We show that X() is non-empty provided that X() is non-empty and X has p-adic points for every prime p. acknowledgement: "EP/F060661/1\tEngineering and Physical Sciences Research Council" author: - first_name: Timothy D full_name: Timothy Browning id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Roger full_name: Heath-Brown, Roger last_name: Heath Brown citation: ama: Browning TD, Heath Brown R. Rational points on quartic hypersurfaces. Journal fur die Reine und Angewandte Mathematik. 2009;(629):37-88. doi:10.1515/CRELLE.2009.026 apa: Browning, T. D., & Heath Brown, R. (2009). Rational points on quartic hypersurfaces. Journal Fur Die Reine Und Angewandte Mathematik. Walter de Gruyter. https://doi.org/10.1515/CRELLE.2009.026 chicago: Browning, Timothy D, and Roger Heath Brown. “Rational Points on Quartic Hypersurfaces.” Journal Fur Die Reine Und Angewandte Mathematik. Walter de Gruyter, 2009. https://doi.org/10.1515/CRELLE.2009.026. ieee: T. D. Browning and R. Heath Brown, “Rational points on quartic hypersurfaces,” Journal fur die Reine und Angewandte Mathematik, no. 629. Walter de Gruyter, pp. 37–88, 2009. ista: Browning TD, Heath Brown R. 2009. Rational points on quartic hypersurfaces. Journal fur die Reine und Angewandte Mathematik. (629), 37–88. mla: Browning, Timothy D., and Roger Heath Brown. “Rational Points on Quartic Hypersurfaces.” Journal Fur Die Reine Und Angewandte Mathematik, no. 629, Walter de Gruyter, 2009, pp. 37–88, doi:10.1515/CRELLE.2009.026. short: T.D. Browning, R. Heath Brown, Journal Fur Die Reine Und Angewandte Mathematik (2009) 37–88. date_created: 2018-12-11T11:45:19Z date_published: 2009-04-01T00:00:00Z date_updated: 2021-01-12T06:56:29Z day: '01' doi: 10.1515/CRELLE.2009.026 extern: 1 issue: '629' main_file_link: - open_access: '1' url: https://arxiv.org/abs/math/0701348 month: '04' oa: 1 page: 37 - 88 publication: Journal fur die Reine und Angewandte Mathematik publication_status: published publisher: Walter de Gruyter publist_id: '7676' quality_controlled: 0 status: public title: Rational points on quartic hypersurfaces type: journal_article year: '2009' ...