Rational torsion points on abelian surfaces with quaternionic multiplication

Jef Laga; Ciaran Schembri; Ari Shnidman; John Voight

doi:https://doi.org/10.1017/fms.2024.105

Rational torsion points on abelian surfaces with quaternionic multiplication

Jef Laga, Ciaran Schembri, Ari Shnidman, John Voight

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	e92
Journal	Forum of Mathematics, Sigma
Volume	12
DOIs	https://doi.org/10.1017/fms.2024.105
State	Published - 8 Nov 2024

All Science Journal Classification (ASJC) codes

Analysis
Theoretical Computer Science
Algebra and Number Theory
Statistics and Probability
Mathematical Physics
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Mathematics

Access to Document

https://doi.org/10.1017/fms.2024.105

Cite this

@article{053ae005eca149979c82a8bf4e3a2da7,

title = "Rational torsion points on abelian surfaces with quaternionic multiplication",

abstract = "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.",

author = "Jef Laga and Ciaran Schembri and Ari Shnidman and John Voight",

note = "Publisher Copyright: {\textcopyright} The Author(s), 2024.",

year = "2024",

month = nov,

day = "8",

doi = "https://doi.org/10.1017/fms.2024.105",

language = "الإنجليزيّة",

volume = "12",

journal = "Forum of Mathematics, Sigma",

issn = "2050-5094",

publisher = "Cambridge University Press",

}

TY - JOUR

T1 - Rational torsion points on abelian surfaces with quaternionic multiplication

AU - Laga, Jef

AU - Schembri, Ciaran

AU - Shnidman, Ari

AU - Voight, John

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 - https://doi.org/10.1017/fms.2024.105

DO - https://doi.org/10.1017/fms.2024.105

M3 - مقالة

SN - 2050-5094

VL - 12

JO - Forum of Mathematics, Sigma

JF - Forum of Mathematics, Sigma

M1 - e92

ER -

Rational torsion points on abelian surfaces with quaternionic multiplication

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this