no. 7
The Brauer group of torsors and its arithmetic applications
[Le groupe de Brauer des torseurs et ses applications arithmétiques]
Harari, David1 ; Skorobogatov, Alexei N.2
1 École Normale Supérieure, DMA, 45 rue d'Ulm, 75230 Paris Cedex 05 (France)
2 Imperial College, Department of Mathematics, 180 Queen's Gate, London SW7 2BZ (Royaume-Uni)
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 : 10.5802/aif.1998
Classification : 11G35, 14G05
Keywords: Brauer group, Hasse principle, universal torsor
Mot clés : groupe de Brauer, principe de Hasse, torseur universel
Harari, David 1 ; Skorobogatov, Alexei N. 2

1 École Normale Supérieure, DMA, 45 rue d'Ulm, 75230 Paris Cedex 05 (France)
2 Imperial College, Department of Mathematics, 180 Queen's Gate, London SW7 2BZ (Royaume-Uni) 
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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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