no. 4
Weak Approximation for Fano Complete Intersections in Positive Characteristic
[L’approximation faible pour les intersections complètes de type Fano en caractéristique positive]
Starr, Jason M.1 ; Tian, Zhiyu2 ; Zong, Runhong3
1 Department of Mathematics Stony Brook University Stony Brook, NY 11794 (USA)
2 Beijing International Center for Mathematical Research Peking University No.5 Yiheyuan Road Beijing, 100871 (China)
3 Department of Mathematics Nanjing University 204 Meng Minwei Building No. 22 Hankou Road Nanjing, Jiangsu, 210093 (China)
Annales de l'Institut Fourier, Tome 72 (2022) no. 4, pp. 1503-1534.

Pour une courbe lisse B sur un corps k=k ¯ de caractéristique positive p, pour chaque intersection complète X B dans B× Speck ℙ k n de type (d 1 ,⋯,d c ), nour prouvons l’approximation faible des points adeliques de X B par des k(B)-points sur toutes les places de forte réduction potentiellement bonne, si l’indice de Fano est au moins deux et si p>max(d 1 ,⋯,d c ). Cela s’applique également aux spécialisations des variétés de Fano complexes de nombre de Picard de rang 1 et d’indice de Fano 1 en dehors de l’ensemble des mauvais nombres premiers.

For a smooth curve B over a field k=k ¯ with char(k)=p, for every complete intersection X B in B× Speck ℙ k n of type (d 1 ,⋯,d c ), we prove weak approximation of adelic points of X B by k(B)-points at all places of (strong) potentially good reduction, if the Fano index is ≥2 and if p>max(d 1 ,⋯,d c ). This also applies to specializations of complex Fano manifolds with Picard rank 1 and Fano index 1 away from “bad primes”.

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DOI : 10.5802/aif.3495
Classification : 14M22, 14D10, 14G12
Keywords: weak approximation, separably rationally connected, stability
Mot clés : approximation faible, séparablement rationnellement connexe, stabilité

Starr, Jason M. 1 ; Tian, Zhiyu 2 ; Zong, Runhong 3

1 Department of Mathematics Stony Brook University Stony Brook, NY 11794 (USA)
2 Beijing International Center for Mathematical Research Peking University No.5 Yiheyuan Road Beijing, 100871 (China)
3 Department of Mathematics Nanjing University 204 Meng Minwei Building No. 22 Hankou Road Nanjing, Jiangsu, 210093 (China)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     journal = {Annales de l'Institut Fourier},
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Starr, Jason M.; Tian, Zhiyu; Zong, Runhong. Weak Approximation for Fano Complete Intersections in Positive Characteristic. Annales de l'Institut Fourier, Tome 72 (2022) no. 4, pp. 1503-1534. doi : 10.5802/aif.3495. https://aif.centre-mersenne.org/articles/10.5802/aif.3495/

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