Abstract

We give a quantitative version of Ribet's famous level lowering result for modular forms. Specifically, we measure how certain congruence ideals change as we vary the level. By studying the deformation theory of the Galois representation attached to the modular form, we can use the numerical criterion of Wiles to relate congruence ideals to Selmer groups, and thereby reduce the problem to a calculation in Galois cohomology.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 419-448
Launched on MUSE
2016-04-04
Open Access
No
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