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Proceedings of the American Mathematical Society

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On component groups of $J_0(N)$
and degeneracy maps

Author: San Ling
Journal: Proc. Amer. Math. Soc. 126 (1998), 3201-3210
MSC (1991): Primary 11G18, 14H40
MathSciNet review: 1469421
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Abstract: 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

Keywords: Modular curves, Jacobians, component groups, degeneracy maps
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
Article copyright: © Copyright 1998 American Mathematical Society