For a smooth curve over a field with , for every complete intersection in of type , we prove weak approximation of adelic points of by -points at all places of (strong) potentially good reduction, if the Fano index is and if . This also applies to specializations of complex Fano manifolds with Picard rank and Fano index away from “bad primes”.
Pour une courbe lisse sur un corps de caractéristique positive , pour chaque intersection complète dans de type , nour prouvons l’approximation faible des points adeliques de par des -points sur toutes les places de forte réduction potentiellement bonne, si l’indice de Fano est au moins deux et si . Cela s’applique également aux spécialisations des variétés de Fano complexes de nombre de Picard de rang et d’indice de Fano en dehors de l’ensemble des mauvais nombres premiers.
Revised:
Accepted:
Published online:
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
@article{AIF_2022__72_4_1503_0, author = {Starr, Jason M. and Tian, Zhiyu and Zong, Runhong}, title = {Weak {Approximation} for {Fano} {Complete} {Intersections} in {Positive} {Characteristic}}, journal = {Annales de l'Institut Fourier}, pages = {1503--1534}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {72}, number = {4}, year = {2022}, doi = {10.5802/aif.3495}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3495/} }
TY - JOUR AU - Starr, Jason M. AU - Tian, Zhiyu AU - Zong, Runhong TI - Weak Approximation for Fano Complete Intersections in Positive Characteristic JO - Annales de l'Institut Fourier PY - 2022 SP - 1503 EP - 1534 VL - 72 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3495/ DO - 10.5802/aif.3495 LA - en ID - AIF_2022__72_4_1503_0 ER -
%0 Journal Article %A Starr, Jason M. %A Tian, Zhiyu %A Zong, Runhong %T Weak Approximation for Fano Complete Intersections in Positive Characteristic %J Annales de l'Institut Fourier %D 2022 %P 1503-1534 %V 72 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3495/ %R 10.5802/aif.3495 %G en %F AIF_2022__72_4_1503_0
Starr, Jason M.; Tian, Zhiyu; Zong, Runhong. Weak Approximation for Fano Complete Intersections in Positive Characteristic. Annales de l'Institut Fourier, Volume 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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