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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2308.15193 |
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| _version_ | 1866910704744792064 |
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| author | Laga, Jef Schembri, Ciaran Shnidman, Ari Voight, John |
| author_facet | Laga, Jef Schembri, Ciaran Shnidman, Ari Voight, John |
| contents | Let $A$ be an abelian surface over $\mathbb{Q}$ whose geometric endomorphism ring is a maximal order in a non-split quaternion algebra. Inspired by Mazur's theorem for elliptic curves, we show that the torsion subgroup of $A(\mathbb{Q})$ is $12$-torsion and has order at most $18$. Under the additional assumption that $A$ is of $\mathrm{GL}_2$-type, we give a complete classification of the possible torsion subgroups of $A(\mathbb{Q})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_15193 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rational torsion points on abelian surfaces with quaternionic multiplication Laga, Jef Schembri, Ciaran Shnidman, Ari Voight, John Number Theory 14K15 (Primary) 14G05, 11G10 (Secondary) Let $A$ be an abelian surface over $\mathbb{Q}$ whose geometric endomorphism ring is a maximal order in a non-split quaternion algebra. Inspired by Mazur's theorem for elliptic curves, we show that the torsion subgroup of $A(\mathbb{Q})$ is $12$-torsion and has order at most $18$. Under the additional assumption that $A$ is of $\mathrm{GL}_2$-type, we give a complete classification of the possible torsion subgroups of $A(\mathbb{Q})$. |
| title | Rational torsion points on abelian surfaces with quaternionic multiplication |
| topic | Number Theory 14K15 (Primary) 14G05, 11G10 (Secondary) |
| url | https://arxiv.org/abs/2308.15193 |