{"intvolume":" 19","oa":1,"article_processing_charge":"No","issue":"2","year":"2017","type":"journal_article","main_file_link":[{"url":"https://arxiv.org/abs/1403.5937","open_access":"1"}],"page":"357 - 394","volume":19,"month":"01","oa_version":"Preprint","language":[{"iso":"eng"}],"title":"Forms in many variables and differing degrees","quality_controlled":"1","acknowledgement":"While working on this paper the first author was supported by ERC grant 306457.","date_updated":"2024-03-05T11:47:15Z","doi":"10.4171/JEMS/668","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Journal of the European Mathematical Society","date_created":"2018-12-11T11:45:31Z","article_type":"original","extern":"1","_id":"266","abstract":[{"text":"We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a smooth and geometrically integral variety X Pm, provided only that its dimension is large enough in terms of its degree.","lang":"eng"}],"citation":{"ieee":"T. D. Browning and R. Heath Brown, “Forms in many variables and differing degrees,” Journal of the European Mathematical Society, vol. 19, no. 2. European Mathematical Society Publishing House, pp. 357–394, 2017.","ista":"Browning TD, Heath Brown R. 2017. Forms in many variables and differing degrees. Journal of the European Mathematical Society. 19(2), 357–394.","ama":"Browning TD, Heath Brown R. Forms in many variables and differing degrees. Journal of the European Mathematical Society. 2017;19(2):357-394. doi:10.4171/JEMS/668","short":"T.D. Browning, R. Heath Brown, Journal of the European Mathematical Society 19 (2017) 357–394.","chicago":"Browning, Timothy D, and Roger Heath Brown. “Forms in Many Variables and Differing Degrees.” Journal of the European Mathematical Society. European Mathematical Society Publishing House, 2017. https://doi.org/10.4171/JEMS/668.","apa":"Browning, T. D., & Heath Brown, R. (2017). Forms in many variables and differing degrees. Journal of the European Mathematical Society. European Mathematical Society Publishing House. https://doi.org/10.4171/JEMS/668","mla":"Browning, Timothy D., and Roger Heath Brown. “Forms in Many Variables and Differing Degrees.” Journal of the European Mathematical Society, vol. 19, no. 2, European Mathematical Society Publishing House, 2017, pp. 357–94, doi:10.4171/JEMS/668."},"author":[{"last_name":"Browning","first_name":"Timothy D","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Heath Brown","first_name":"Roger","full_name":"Heath Brown, Roger"}],"day":"26","external_id":{"arxiv":["1403.5937"]},"status":"public","date_published":"2017-01-26T00:00:00Z","publist_id":"7636","publisher":"European Mathematical Society Publishing House","publication_status":"published"}