{"date_created":"2018-12-11T11:45:32Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"oa_version":"Submitted Version","publisher":"Societe Mathematique de France","status":"public","quality_controlled":"1","title":"Norm forms for arbitrary number fields as products of linear polynomials","day":"01","type":"journal_article","date_updated":"2024-03-05T12:13:35Z","month":"12","article_processing_charge":"No","issue":"6","publication_status":"published","date_published":"2017-12-01T00:00:00Z","extern":"1","abstract":[{"lang":"eng","text":"Given a number field K/Q and a polynomial P ε Q [t], all of whose roots are Q, let X be the variety defined by the equation NK (x) = P (t). Combining additive combinatiorics with descent we show that the Brauer-Manin obstruction is the only obstruction to the Hesse principle and weak approximation on any smooth and projective model of X."}],"main_file_link":[{"open_access":"1","url":"https://research-information.bristol.ac.uk/en/publications/norm-forms-for-arbitrary-number-fields-as-products-of-linear-polynomials(f79a584b-ec58-47c8-aa97-8c5505e3f751).html"}],"publist_id":"7630","volume":50,"intvolume":"        50","year":"2017","acknowledgement":"While working on this paper the first author was supported by ERC grant 306457 and the second author was supported by EPSRC grant EP/E053262/1 and by ERC grant 208091. Some of this work was carried out during the programme “Arithmetic and geometry” in 2013 at the Hausdorff Institute in Bonn.","doi":"10.24033/asens.2348","page":"1383 - 1446","author":[{"full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","first_name":"Timothy D","orcid":"0000-0002-8314-0177"},{"last_name":"Matthiesen","first_name":"Lilian","full_name":"Matthiesen, Lilian"}],"publication":"Annales Scientifiques de l'Ecole Normale Superieure","citation":{"short":"T.D. Browning, L. Matthiesen, Annales Scientifiques de l’Ecole Normale Superieure 50 (2017) 1383–1446.","ama":"Browning TD, Matthiesen L. Norm forms for arbitrary number fields as products of linear polynomials. <i>Annales Scientifiques de l’Ecole Normale Superieure</i>. 2017;50(6):1383-1446. doi:<a href=\"https://doi.org/10.24033/asens.2348\">10.24033/asens.2348</a>","ista":"Browning TD, Matthiesen L. 2017. Norm forms for arbitrary number fields as products of linear polynomials. Annales Scientifiques de l’Ecole Normale Superieure. 50(6), 1383–1446.","chicago":"Browning, Timothy D, and Lilian Matthiesen. “Norm Forms for Arbitrary Number Fields as Products of Linear Polynomials.” <i>Annales Scientifiques de l’Ecole Normale Superieure</i>. Societe Mathematique de France, 2017. <a href=\"https://doi.org/10.24033/asens.2348\">https://doi.org/10.24033/asens.2348</a>.","apa":"Browning, T. D., &#38; Matthiesen, L. (2017). Norm forms for arbitrary number fields as products of linear polynomials. <i>Annales Scientifiques de l’Ecole Normale Superieure</i>. Societe Mathematique de France. <a href=\"https://doi.org/10.24033/asens.2348\">https://doi.org/10.24033/asens.2348</a>","ieee":"T. D. Browning and L. Matthiesen, “Norm forms for arbitrary number fields as products of linear polynomials,” <i>Annales Scientifiques de l’Ecole Normale Superieure</i>, vol. 50, no. 6. Societe Mathematique de France, pp. 1383–1446, 2017.","mla":"Browning, Timothy D., and Lilian Matthiesen. “Norm Forms for Arbitrary Number Fields as Products of Linear Polynomials.” <i>Annales Scientifiques de l’Ecole Normale Superieure</i>, vol. 50, no. 6, Societe Mathematique de France, 2017, pp. 1383–446, doi:<a href=\"https://doi.org/10.24033/asens.2348\">10.24033/asens.2348</a>."},"article_type":"original","language":[{"iso":"eng"}],"_id":"272"}