Weak Approximation for Fano Complete Intersections in Positive Characteristic
Annales de l'Institut Fourier, Online first, 32 p.

For a smooth curve B over a field k=k ¯ with char(k)=p, for every complete intersection X B in B× Speck 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”.

Pour une courbe lisse B sur un corps k=k ¯ de caractéristique positive p, pour chaque intersection complète X B dans B× Speck 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.

Received:
Revised:
Accepted:
Online First:
DOI: 10.5802/aif.3495
Classification: 14M22,  14D10,  14G12
Keywords: weak approximation, separably rationally connected, stability
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)
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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, Online first, 32 p.

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