Level Lowering via the Deformation theory of Galois Representations
Anwesh Ray (University of British Columbia)
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
Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).
We acknowledge the support of PIMS, NSERC, and SFU.
For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.
We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca
| Organizer: | Katrina Honigs* |
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