no. 2
The density of fibres with a rational point for a fibration over hypersurfaces of low degree
[La densité des fibres possédant un point rationnel pour une fibration au-dessus d’une hypersurface de bas degré]
Sofos, Efthymios1 ; Visse-Martindale, Erik2
1 The Mathematics and Statistics Building University of Glasgow University Place Glasgow, G12 8QQ (Scotland)
2 Universiteit Leiden Mathematisch Instituut Niels Bohrweg 1, Leiden 2333 CA (Netherlands)
Annales de l'Institut Fourier, Tome 71 (2021) no. 2, pp. 679-709.

Nous établissons une formule asymptotique concernant la proportion de fibres possédant un point rationnel dans le cas d’une fibration en coniques, la base de la fibration étant une hypersurface générique de bas degré.

We prove asymptotics for the proportion of fibres with a rational point in a conic bundle fibration. The base of the fibration is a general hypersurface of low degree.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3413
Classification : 14G05, 14D06, 11P55, 14D10
Keywords: Hardy-Littlewood circle method, Serre’s problem, fibres with a rational point
Mot clés : Méthode du cercle de Hardy-Littlewood, Le problème de Serre, Fibres possédant un point rationnel
Sofos, Efthymios 1 ; Visse-Martindale, Erik 2

1 The Mathematics and Statistics Building University of Glasgow University Place Glasgow, G12 8QQ (Scotland)
2 Universiteit Leiden Mathematisch Instituut Niels Bohrweg 1, Leiden 2333 CA (Netherlands)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {The density of fibres with a rational point for a fibration over hypersurfaces of low degree},
     journal = {Annales de l'Institut Fourier},
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     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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Sofos, Efthymios; Visse-Martindale, Erik. The density of fibres with a rational point for a fibration over hypersurfaces of low degree. Annales de l'Institut Fourier, Tome 71 (2021) no. 2, pp. 679-709. doi : 10.5802/aif.3413. https://aif.centre-mersenne.org/articles/10.5802/aif.3413/

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