A computational approach to the 2-torsion structure of abelian threefolds

Author:
John Cullinan

Journal:
Math. Comp. **78** (2009), 1825-1836

MSC (2000):
Primary 11G10

DOI:
https://doi.org/10.1090/S0025-5718-09-02218-2

Published electronically:
January 22, 2009

MathSciNet review:
2501078

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Abstract: Let be a three-dimensional abelian variety defined over a number field . Using techniques of group theory and explicit computations with MAGMA, we show that if has an even number of -rational points for almost all primes of , then there exists a -isogenous which has an even number of -rational torsion points. We also show that there exist abelian varieties of all dimensions such that is even for almost all primes of , but there does not exist a -isogenous such that is even.

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Additional Information

**John Cullinan**

Affiliation:
Department of Mathematics, Bard College, P.O. Box 5000, Annandale-on-Hudson, New York 12504

Email:
cullinan@bard.edu

DOI:
https://doi.org/10.1090/S0025-5718-09-02218-2

Keywords:
Abelian variety,
torsion points

Received by editor(s):
February 26, 2007

Received by editor(s) in revised form:
August 2, 2008

Published electronically:
January 22, 2009

Article copyright:
© Copyright 2009
American Mathematical Society