Geodesic
On the rationality problem for conic bundles
Sbornik. Mathematics, Tome 72 (1992) no. 1, pp. 105-111

Voir la notice de l'article provenant de la source Math-Net.Ru

For a standard conic bundle over a rational surface the equivalence of two different pairs of conditions sufficient for rationality is proved, along with the necessity of certain weaker conditions. 
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V. A. Iskovskikh. On the rationality problem for conic bundles. Sbornik. Mathematics, Tome 72 (1992) no. 1, pp. 105-111. http://geodesic.mathdoc.fr/item/SM_1992_72_1_a4/