no. 7
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, pp. 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 
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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/articles/10.5802/aif.1998/

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