Rational Points On Certain Abelian Varieties Over Function Fields

Hazama, Fumio

doi:10.1006/jnth.1995.1022

Cited by 11 publications

(16 citation statements)

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“…In [32], Ulmer related the Mordell-Weil group of certain Jacobian varieties over k 0 (t), where k 0 is an arbitrary field, with the group of homomorphisms of other Jacobian varieties. We note that a similar result has been proved by several authors in the literature with different methods [6,15,21,34]. He also showed the unboundedness of the rank of elliptic curves overF p (t) by providing an concrete example of elliptic curve of large rank with the explicit independent points.…”

Section: Introductionsupporting

confidence: 79%

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

Salami¹

2021

Journal De Théorie Des Nombres De Bordeaux

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Twists of the Albanese varieties of cyclic multiple planes with large ranks over higher dimension function fields Tome 32, n o 3 (2020), p. 861-876. © Société Arithmétique de Bordeaux, 2020, tous droits réservés. L'accès aux articles de la revue « Journal de Théorie des Nombres de Bordeaux » (http://jtnb.centre-mersenne.org/), implique l'accord avec les conditions générales d'utilisation (http://jtnb. centre-mersenne.org/legal/). Toute reproduction en tout ou partie de cet article sous quelque forme que ce soit pour tout usage autre que l'utilisation à fin strictement personnelle du copiste est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. cedram Article mis en ligne dans le cadre du Centre de diffusion des revues académiques de mathématiques http://www.centre-mersenne.org/ Journal de Théorie des Nombres de Bordeaux 32 (2020), 861-876 Twists of the Albanese varieties of cyclic multiple planes with large ranks over higher dimension function fields par Sajad SALAMI Résumé. 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.

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Section: Introductionsupporting

confidence: 79%

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

Salami¹

2021

Journal De Théorie Des Nombres De Bordeaux

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“…In this paper, we generalize the main result of Hazama in [5] to an arbitrary cyclic s-covers of irreducible quasi-projective varieties for any integer s ≥ 2. We fix a global field k of characteristic ≥ 0 not dividing s, so that it contains an s-th root of unity, which is denoted by ζ.…”

Section: Introduction and Main Resultsmentioning

confidence: 79%

“…In [4,5], Hazama gave an explicit method of construction of Abelian varieties that have large rank over function fields using the twist theory [2,4]. In [16], Wang extended the result of [4] to cyclic covers of the projective line with prime degrees.…”

Section: The Results Of Hazamamentioning

confidence: 99%

The rational points on certain Abelian varieties over function fields

Salami

2019

Journal of Number Theory

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In this paper, we consider Abelian varieties over function fields that arise as twists of Abelian varieties by cyclic covers of irreducible quasiprojective varieties. Then, in terms of Prym varieties associated to the cyclic covers, we prove a structure theorem on their Mordell-Weil group. Our results give an explicit method for construction of elliptic curves, hyper-and super-elliptic Jacobians that have large ranks over function fields of certain varieties.

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“…The present paper is a generalization of the work of Salami in [5] to arbitrary Galois coverings. More precisely, let n ∈ N be a natural number such that the characteristic of the field k in the previous paragraph does not divide n and k contains a primitive n-th root of unity ξ.…”

Section: Introduction Letmentioning

confidence: 98%