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Conjectural estimates on the Mordell-Wei...

Ortiz, Andrea Surroc...

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Conjectural estimates on the Mordell-Weil and Tate-Shafarevich groups of an abelian variety by Ortiz, Andrea Surroca ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	01-08-2023
Summary	We consider an abelian variety defined over a number field. We give conditional bounds for the order of its Tate-Shafarevich group, as well as conditional bounds for the N\'eron-Tate height of generators of its Mordell-Weil group. The bounds are implied by strong but nowadays classical conjectures, such as the Birch and Swinnerton-Dyer conjecture and the functional equation of the L-series. In particular, we improve and generalise a result by D. Goldfeld and L. Szpiro on the order of the Tate-Shafarevich group, and extends a conjecture of S. Lang on the canonical height of a system of generators of the free part of the Mordell-Weil group. The method is an extension of the algorithm proposed by Yu. Manin for finding a basis for the non-torsion rational points of an elliptic curve defined over the rationals.
ISBN	-
Item Type	Article
File Type	pdf
File Size	29.34 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/0801.1054

Citation

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AMA 11th EditionReferences

Ortiz, Andrea Surroca. Conjectural estimates on the Mordell-Weil and Tate-Shafarevich groups of an abelian variety. Australian National University. August 01, 2023. Accessed September 20, 2024. https://online.provdatabase.com/cite/1993

APA 7th EditionReferences

Ortiz, Andrea Surroca. (2023). Conjectural estimates on the Mordell-Weil and Tate-Shafarevich groups of an abelian variety. Australian National University. https://online.provdatabase.com/cite/1993

Chicago 17th EditionReferences

Ortiz, Andrea Surroca. Conjectural estimates on the Mordell-Weil and Tate-Shafarevich groups of an abelian variety. Australian National University. 2023. https://online.provdatabase.com/cite/1993

HarvardReferences

Ortiz, Andrea Surroca. (2023). Conjectural estimates on the Mordell-Weil and Tate-Shafarevich groups of an abelian variety. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/1993. (Accessed 20 September 2024).

Harvard AustraliaReferences

Ortiz, Andrea Surroca, 2023, Conjectural estimates on the Mordell-Weil and Tate-Shafarevich groups of an abelian variety, Australian National University, viewed 20 September 2024, <https://online.provdatabase.com/cite/1993>

MLA 9th EditionWorks Cited

Ortiz, Andrea Surroca. Conjectural estimates on the Mordell-Weil and Tate-Shafarevich groups of an abelian variety. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/1993.

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