Twists of the Albanese varieties of cyclic multiple planes with large ranks over higher dimension function fields

Salami, Sajad

Journal de théorie des nombres de Bordeaux, Tome 32 (2020) no. 3, pp. 861-876.

Dans [17], nous avons prouvé un théorème de structure pour les groupes de Mordell–Weil de variétés abéliennes définies sur des corps de fonctions, obtenues comme tordues de variétés abéliennes par des revêtements cycliques de variétés projectives, et ce en terme des variétés de Prym associées à ces revêtements. Dans ce nouvel article, nous donnons une méthode explicite pour construire des variétés abéliennes de grands rangs sur les corps de fonctions. Pour ce faire, nous appliquons le théorème mentionné ci-dessus aux twists des variétés d’Albanese des plans multiples cycliques.

In [17], we proved a structure theorem on the Mordell–Weil group of abelian varieties over function fields that arise as the twists of abelian varieties by the cyclic covers of projective varieties in terms of the Prym varieties associated with covers. In this paper, we provide an explicit way to construct the abelian varieties with large ranks over the higher dimension function fields. To do so, we apply the above-mentioned theorem to the twists of Albanese varieties of the cyclic multiple planes.

Classification : 11G10, 14H40, 14H05
Mots clés : Mordell–Weil rank, Twists, Albanese and Prym varieties, Cyclic multiple planes, Higher dimension function fields

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