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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the rational cuspidal subgroup and the rational torsion points of $J_0(pq)$
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by Seng-Kiat Chua and San Ling PDF
Proc. Amer. Math. Soc. 125 (1997), 2255-2263 Request permission

Abstract:

For two distinct prime numbers $p$, $q$, we compute the rational cuspidal subgroup $C(pq)$ of $J_0(pq)$ and determine the $\ell$-primary part of the rational torsion subgroup of the old subvariety of $J_0(pq)$ for most primes $\ell$. Some results of Berkovič on the nontriviality of the Mordell-Weil group of some Eisenstein factors of $J_0(pq)$ are also refined.
References
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Additional Information
  • Seng-Kiat Chua
  • Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Republic of Singapore
  • Email: matchua@nus.sg
  • San Ling
  • Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Republic of Singapore
  • Email: matlings@nus.sg
  • Received by editor(s): September 8, 1995
  • Received by editor(s) in revised form: March 10, 1996
  • Additional Notes: The authors would like to thanks Ken Ribet for private communication. We are also grateful to the referee for comments which helped improve the presentation of the paper.
  • Communicated by: William W. Adams
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 2255-2263
  • MSC (1991): Primary 11G18, 11F03, 11F20, 14H40
  • DOI: https://doi.org/10.1090/S0002-9939-97-03874-4
  • MathSciNet review: 1396972