{"article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","language":[{"iso":"eng"}],"oa":1,"publist_id":"7636","external_id":{"arxiv":["1403.5937"]},"date_published":"2017-01-26T00:00:00Z","year":"2017","publisher":"European Mathematical Society Publishing House","date_updated":"2024-03-05T11:47:15Z","extern":"1","publication_status":"published","article_processing_charge":"No","page":"357 - 394","type":"journal_article","intvolume":"        19","author":[{"full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","orcid":"0000-0002-8314-0177","first_name":"Timothy D"},{"first_name":"Roger","full_name":"Heath Brown, Roger","last_name":"Heath Brown"}],"date_created":"2018-12-11T11:45:31Z","title":"Forms in many variables and differing degrees","day":"26","issue":"2","citation":{"apa":"Browning, T. D., &#38; Heath Brown, R. (2017). Forms in many variables and differing degrees. <i>Journal of the European Mathematical Society</i>. European Mathematical Society Publishing House. <a href=\"https://doi.org/10.4171/JEMS/668\">https://doi.org/10.4171/JEMS/668</a>","ieee":"T. D. Browning and R. Heath Brown, “Forms in many variables and differing degrees,” <i>Journal of the European Mathematical Society</i>, vol. 19, no. 2. European Mathematical Society Publishing House, pp. 357–394, 2017.","mla":"Browning, Timothy D., and Roger Heath Brown. “Forms in Many Variables and Differing Degrees.” <i>Journal of the European Mathematical Society</i>, vol. 19, no. 2, European Mathematical Society Publishing House, 2017, pp. 357–94, doi:<a href=\"https://doi.org/10.4171/JEMS/668\">10.4171/JEMS/668</a>.","chicago":"Browning, Timothy D, and Roger Heath Brown. “Forms in Many Variables and Differing Degrees.” <i>Journal of the European Mathematical Society</i>. European Mathematical Society Publishing House, 2017. <a href=\"https://doi.org/10.4171/JEMS/668\">https://doi.org/10.4171/JEMS/668</a>.","ista":"Browning TD, Heath Brown R. 2017. Forms in many variables and differing degrees. Journal of the European Mathematical Society. 19(2), 357–394.","short":"T.D. Browning, R. Heath Brown, Journal of the European Mathematical Society 19 (2017) 357–394.","ama":"Browning TD, Heath Brown R. Forms in many variables and differing degrees. <i>Journal of the European Mathematical Society</i>. 2017;19(2):357-394. doi:<a href=\"https://doi.org/10.4171/JEMS/668\">10.4171/JEMS/668</a>"},"publication":"Journal of the European Mathematical Society","volume":19,"status":"public","oa_version":"Preprint","_id":"266","acknowledgement":"While working on this paper the first author was supported by ERC grant 306457.","main_file_link":[{"url":"https://arxiv.org/abs/1403.5937","open_access":"1"}],"doi":"10.4171/JEMS/668","month":"01","abstract":[{"lang":"eng","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."}]}