Level Lowering via the Deformation theory of Galois Representations

Abstract: Elliptic curves defined over the rational numbers arise from certain modular forms. This is the celebrated Modularity theorem of Wiles et al. Prior to this development, Ribet had proved a level lowering theorem, thanks to which one is able to optimize the level of the modular form in question. Ribet's theorem combined with the modularity theorem of Wiles together imply Fermat's Last theorem.

In joint work with Ravi Ramakrishna, we develop some new techniques to prove level lowering results for more general Galois representations.

algebraic geometrynumber theory

Audience: researchers in the topic

SFU NT-AG seminar

Series comments: Description: Research/departmental seminar

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