Norm forms for arbitrary number fields as products of linear polynomials
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.
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Author
Browning, Timothy DISTA 
;
Matthiesen, Lilian
;
Matthiesen, LilianCorresponding author has ISTA affiliation
Abstract
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.
Publishing Year
Date Published
2017-12-01
Journal Title
Annales Scientifiques de l'Ecole Normale Superieure
Publisher
Societe Mathematique de France
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.
Volume
50
Issue
6
Page
1383 - 1446
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Cite this
Browning TD, Matthiesen L. Norm forms for arbitrary number fields as products of linear polynomials. Annales Scientifiques de l’Ecole Normale Superieure. 2017;50(6):1383-1446. doi:10.24033/asens.2348
Browning, T. D., & Matthiesen, L. (2017). Norm forms for arbitrary number fields as products of linear polynomials. Annales Scientifiques de l’Ecole Normale Superieure. Societe Mathematique de France. https://doi.org/10.24033/asens.2348
Browning, Timothy D, and Lilian Matthiesen. “Norm Forms for Arbitrary Number Fields as Products of Linear Polynomials.” Annales Scientifiques de l’Ecole Normale Superieure. Societe Mathematique de France, 2017. https://doi.org/10.24033/asens.2348.
T. D. Browning and L. Matthiesen, “Norm forms for arbitrary number fields as products of linear polynomials,” Annales Scientifiques de l’Ecole Normale Superieure, vol. 50, no. 6. Societe Mathematique de France, pp. 1383–1446, 2017.
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.
Browning, Timothy D., and Lilian Matthiesen. “Norm Forms for Arbitrary Number Fields as Products of Linear Polynomials.” Annales Scientifiques de l’Ecole Normale Superieure, vol. 50, no. 6, Societe Mathematique de France, 2017, pp. 1383–446, doi:10.24033/asens.2348.
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