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30/09/2013, 15:00 — 16:00 — Room P3.10, Mathematics Building

Nuno Freitas, *Univ. Bayreuth*

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The Fermat equation over totally real number fields

Jarvis and Meekin have shown that the classical Fermat equation
\(x^p + y^p = z^p\) has no non-trivial solutions over
\(\mathbb{Q}(\sqrt{2})\). This is the only result available over
number fields. Two major obstacles to attack the equation over
other number fields are the modularity of the Frey curves and the
existence of newforms in the spaces obtained after level
lowering.

In this talk, we will describe how we deal with these
obstacles, using recent modularity lifting theorems and level
lowering. In particular, we will solve the equation for infinitely
many real quadratic fields.