The Brauer group of torsors and its arithmetic applications  [ Le groupe de Brauer des torseurs et ses applications arithmétiques ]
Annales de l'Institut Fourier, Tome 53 (2003) no. 7, p. 1987-2019
Soit X une variété algébrique définie sur un corps de caractéristique zéro k. Soit Y un X-torseur sous un tore. Nous calculons le groupe de Brauer de Y et nous en déduisons des conséquences arithmétiques pour X quand k est un corps de nombres.
Let X be an algebraic variety defined over a field k of characteristic 0, and let Y be an X-torsor under a torus. We compute the Brauer group of Y. In the case of a number field k we deduce results concerning the arithmetic of X.
DOI : https://doi.org/10.5802/aif.1998
Classification:  11G35,  14G05
Mots clés: groupe de Brauer, principe de Hasse, torseur universel
@article{AIF_2003__53_7_1987_0,
     author = {Harari, David and Skorobogatov, Alexei N.},
     title = {The Brauer group of torsors and its arithmetic applications},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {7},
     year = {2003},
     pages = {1987-2019},
     doi = {10.5802/aif.1998},
     zbl = {02093464},
     mrnumber = {2044165},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2003__53_7_1987_0}
}
Harari, David; Skorobogatov, Alexei N. The Brauer group of torsors and its arithmetic applications. Annales de l'Institut Fourier, Tome 53 (2003) no. 7, pp. 1987-2019. doi : 10.5802/aif.1998. http://www.numdam.org/item/AIF_2003__53_7_1987_0/

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