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Topological Quantum Field Theory Seminar   RSS

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

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.


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Current organizers: José MourãoRoger Picken, Marko Stošić

Mathseminars

FCT Projects PTDC/MAT-GEO/3319/2014, Quantization and Kähler Geometry, PTDC/MAT-PUR/31089/2017, Higher Structures and Applications.

CAMGSD FCT