On component groups of 𝐽₀(𝑁) and degeneracy maps

Ling, San

doi:10.1090/S0002-9939-98-04592-4

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

Proc. Amer. Math. Soc. 126 (1998), 3201-3210

DOI: https://doi.org/10.1090/S0002-9939-98-04592-4

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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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