Autor: |
Jef Laga, Ciaran Schembri, Ari Shnidman, John Voight |
Jazyk: |
angličtina |
Rok vydání: |
2024 |
Předmět: |
|
Zdroj: |
Forum of Mathematics, Sigma, Vol 12 (2024) |
Druh dokumentu: |
article |
ISSN: |
2050-5094 |
DOI: |
10.1017/fms.2024.105 |
Popis: |
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 $A({\mathbb {Q}})$ . |
Databáze: |
Directory of Open Access Journals |
Externí odkaz: |
|