Generalized Fermat equations over totally real fields

Abstract: Wiles’ famous proof of Fermat’s Last Theorem pioneered the so-called modular method, in which modularity of elliptic curves is used to show that all integer solutions of Fermat’s equation are trivial.

In this talk, we briefly sketch a variant of the modular method described by Freitas and Siksek in 2014, proving that for sufficiently large exponents, Fermat’s Last Theorem holds in five-sixths of real quadratic fields. We then extend this method to explore solutions to two broader Fermat-type families of equations. The main ingredients are modularity, level lowering, image of inertia comparisons, and S-unit equations.

algebraic geometrynumber theory

Audience: researchers in the discipline

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SFU NT-AG seminar

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

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