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Mathematics of Computation

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$ p^k$-torsion of genus two curves over $ \mathbb{F}_{p^m}$


Author: Michael E. Zieve
Journal: Math. Comp. 79 (2010), 1833-1838
MSC (2010): Primary 14H40
DOI: https://doi.org/10.1090/S0025-5718-10-02305-7
Published electronically: January 14, 2010
MathSciNet review: 2630016
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Abstract: We determine the isogeny classes of abelian surfaces over $ \mathbb{F}_q$ whose group of $ \mathbb{F}_q$-rational points has order divisible by $ q^2$. We also solve the same problem for Jacobians of genus-$ 2$ curves.


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Additional Information

Michael E. Zieve
Affiliation: Department of Mathematics, Hill Center–Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854–8019
Address at time of publication: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043
Email: zieve@umich.edu

DOI: https://doi.org/10.1090/S0025-5718-10-02305-7
Received by editor(s): May 29, 2007
Received by editor(s) in revised form: August 30, 2008
Published electronically: January 14, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.