Geodesic
Rational points on pencils of conics and quadrics with many degenerate fibres
Tim D. Browning1 ; Lilian Matthiesen2 ; Alexei N. Skorobogatov3
1 School of Mathematics, University of Bristol, Bristol BS8, 1TW, Bristol U.K.
2 Institut de Mathématiques de Jussieu --- Paris Rive Gauche, 75205 Paris Cedex 13, France
3 Imperial College London, London SW7 2AZ, United Kingdom and<br/> Institute for the Information Transmission Problems, Moscow, Russia
Annals of mathematics, Tome 180 (2014) no. 1, pp. 381-402.

Voir la notice de l'article provenant de la source Annals of Mathematics website

For any pencil of conics or higher-dimensional quadrics over $\mathbb{Q}$, with all degenerate fibres defined over $\mathbb{Q}$, we show that the Brauer–Manin obstruction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics over $\mathbb{Q}$, which is a consequence of recent advances in additive combinatorics.
DOI : 10.4007/annals.2014.180.1.8

Tim D. Browning 1 ; Lilian Matthiesen 2 ; Alexei N. Skorobogatov 3

1 School of Mathematics, University of Bristol, Bristol BS8, 1TW, Bristol U.K.
2 Institut de Mathématiques de Jussieu --- Paris Rive Gauche, 75205 Paris Cedex 13, France
3 Imperial College London, London SW7 2AZ, United Kingdom and<br/> Institute for the Information Transmission Problems, Moscow, Russia 
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Tim D. Browning; Lilian Matthiesen; Alexei N. Skorobogatov. Rational points on pencils of conics and quadrics with many degenerate fibres. Annals of mathematics, Tome 180 (2014) no. 1, pp. 381-402. doi : 10.4007/annals.2014.180.1.8. http://geodesic.mathdoc.fr/articles/10.4007/annals.2014.180.1.8/

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