TY - JOUR
T1 - Rational torsion points on abelian surfaces with quaternionic multiplication
AU - Laga, Jef
AU - Schembri, Ciaran
AU - Shnidman, Ari
AU - Voight, John
N1 - Publisher Copyright:
© The Author(s), 2024.
PY - 2024/11/8
Y1 - 2024/11/8
N2 - Let A be an abelian surface over 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 is -torsion and has order at most. Under the additional assumption that A is of -type, we give a complete classification of the possible torsion subgroups of.
AB - Let A be an abelian surface over 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 is -torsion and has order at most. Under the additional assumption that A is of -type, we give a complete classification of the possible torsion subgroups of.
UR - http://www.scopus.com/inward/record.url?scp=85209357638&partnerID=8YFLogxK
U2 - 10.1017/fms.2024.105
DO - 10.1017/fms.2024.105
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85209357638
SN - 2050-5094
VL - 12
JO - Forum of Mathematics, Sigma
JF - Forum of Mathematics, Sigma
M1 - e92
ER -