Soit une variété algébrique définie sur un corps de caractéristique zéro . Soit un -torseur sous un tore. Nous calculons le groupe de Brauer de et nous en déduisons des conséquences arithmétiques pour quand est un corps de nombres.
Let be an algebraic variety defined over a field of characteristic , and let be an -torsor under a torus. We compute the Brauer group of . In the case of a number field we deduce results concerning the arithmetic of .
@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}, volume = {53}, year = {2003}, pages = {1987-2019}, doi = {10.5802/aif.1998}, mrnumber = {2044165}, zbl = {02093464}, language = {en}, url = {http://dml.mathdoc.fr/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) pp. 1987-2019. doi : 10.5802/aif.1998. http://gdmltest.u-ga.fr/item/AIF_2003__53_7_1987_0/
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