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The old subvariety of Jo(pq)

  • Kenneth A. Ribet
Chapter
Part of the Progress in Mathematics book series (PM, volume 89)

Abstract

Let p and q be distinct primes. The old part of J o (pq) is the abelian subvariety A + B of J o (pq) generated by the images
$$ A = {\rm Im} age({J_0}{(p)^2}\xrightarrow{\alpha }{J_0}(pq)),B = {\rm Im} age({J_0}({q^2})\xrightarrow{\beta }{J_0}(pq)) $$
of the two indicated degeneracy maps. Here, J o (N) denotes the Jacobian Pic°(X o (N)) of the standard modular curve X o (N), for each integer N ≥ 1. Also, we have written J o (p)2 for the product J o (p) × J o (p), and have used analogous notation for J o (q)2. The definitions of α and β will be given below; see also [6], §2a.

Keywords

Exact Sequence Modular Form Abelian Variety Cyclic Subgroup Modular Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Science+Business Media New York 1991

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  • Kenneth A. Ribet

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