Seminário de Teoria Quântica do Campo Topológica   RSS

28/09/2012, 14:00 — 15:00 — Sala P4.35, Pavilhão de Matemática
Nuno Freitas, Univ. Barcelona

Fermat-type equations of signature \((13,13,p)\) via Hilbert cuspforms

In this talk I will give an introduction to the modular approach to Fermat-type equations via Hilbert cuspforms and discuss how it can be used to show that certain equations of the form x 13 +y 13 =Cz p have no solutions (a,b,c) such that gcd(a,b)=1 and 13 c if p>4992539 . We will first relate a putative solution of the previous equation to the solution of another Diophantine equation with coefficients in Q(13 ). Then we attach Frey curves E over Q(13 ) to solutions of the latter equation. Finally, we will discuss on the modularity of E and irreducibility of certain Galois representations attached to it. These ingredients enable us to apply a modular approach via Hilbert newforms to get the desired arithmetic result on the equation.
Duration 90 minutes or slightly less

Organizadores correntes: Roger Picken, Marko Stošić.

Projecto FCT PTDC/MAT-GEO/3319/2014, Quantization and Kähler Geometry.