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arXiv · 1502.04460

Principe de Hasse pour les intersections de deux quadriques

Olivier Wittenberg
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Abstract

Admettant l'hypothèse de Schinzel et la finitude des groupes de Tate-Shafarevich des courbes elliptiques sur les corps de nombres, toute intersection lisse de deux quadriques dans l'espace projectif de dimension n satisfait au principe de Hasse si n>4. Le même résultat vaut pour n=4, c'est-à-dire pour les surfaces de del Pezzo de degré 4, lorsque le groupe de Brauer est réduit aux constantes et que la surface est suffisamment générale. ----- Assuming Schinzel's hypothesis and the finiteness of Tate-Shafarevich groups of elliptic curves over number fields, smooth intersections of two quadrics in n-dimensional projective space satisfy the Hasse principle if n>4. The same result holds for n=4, i.e., for del Pezzo surfaces of degree 4, provided the Brauer group is reduced to constants and the surface is sufficiently general.

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Olivier Wittenberg. 2015-02-16. Principe de Hasse pour les intersections de deux quadriques. https://doi.org/10.1016/j.crma.2005.12.005

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