Torsion and twists of abelian varieties

Mentzelos Melistas

doi:10.48550/arXiv.2310.11086

Torsion and twists of abelian varieties

Mentzelos Melistas

Mathematics of Operations Research

Research output: Working paper › Preprint › Academic

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Abstract

In this article, we investigate the possible torsion subgroups of twists of abelian varieties with good reduction. As an application, we prove a theorem concerning ramified primes over any quadratic extension where odd-order torsion growth is achieved. In particular, we show that for every rational elliptic curve and every imaginary quadratic field not equal to $\mathbb{Q}(\sqrt{-3})$ satisfying the Heegner hypothesis no odd-order torsion growth can occur.

Original language	English
Publisher	ArXiv.org
DOIs	https://doi.org/10.48550/arXiv.2310.11086
Publication status	Published - 17 Oct 2023

Keywords

math.NT
math.AG

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10.48550/arXiv.2310.11086

2310.11086v2Final published version, 242 KB

Torsion and twists of abelian varieties
Melistas, M., Feb 2024, In: Bulletin of the London Mathematical Society. 56, 2, p. 589-601 13 p.
Research output: Contribution to journal › Article › Academic › peer-review

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Torsion and twists of abelian varieties

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Torsion and twists of abelian varieties

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