Papers › Rational torsion points on abelian surfaces with quaternionic multiplication
Rational torsion points on abelian surfaces with quaternionic multiplication
Jef Laga, Ciaran Schembri, Ari Shnidman, John Voight
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Let A be an abelian surface over 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(ℚ) is $12$-torsion and has order at most $18$. Under the additional assumption that A is of GL₂-type, we give a complete classification of the possible torsion subgroups of A(ℚ).
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