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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)

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On component groups of $J_0(N)$ and degeneracy maps
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by San Ling PDF
Proc. Amer. Math. Soc. 126 (1998), 3201-3210 Request permission


For an integer $M>1$ and a prime $p \geq 5$ not dividing $M$, we study the kernel of the degeneracy map $\Phi _{Mp,p}^r \rightarrow \Phi _{Mp^r, p}$, where $\Phi _{Mp,p}$ and $\Phi _{Mp^r, p}$ are the component groups of $J_0(Mp)$ and $J_0(Mp^r)$, respectively. This is then used to determine the kernel of the degeneracy map $J_0(Mp)^2 \rightarrow J_0(Mp^2)$ when $J_0(M) =0$. We also compute the group structure of $\Phi _{Mp^2, p}$ in some cases.
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Additional Information
  • San Ling
  • Email:
  • Received by editor(s): April 7, 1997
  • Additional Notes: It is a pleasure to thank Bas Edixhoven for patiently correcting the author’s initial erroneous understanding of some concepts and for the content of §2.1.
  • Communicated by: David E. Rohrlich
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 3201-3210
  • MSC (1991): Primary 11G18, 14H40
  • DOI:
  • MathSciNet review: 1469421