Number Theory Seminar
Local points on twists of X(p)
Speaker: Diana Mocanu (Max Planck Institute, Bonn)Date: Thursday, 22 January 2026 - 12:30Place: Aula 420, Módulo 17, Departamento de Matemáticas, UAM
Abstract:
Let E be a rational elliptic curve and p an odd prime. The modular curve X_E^-(p) parametrizes elliptic curves with p-torsion modules anti-symplectically isomorphic to E[p]. In this talk, I present my recent work with Nuno Freitas on a complete classification for when these curves admit points everywhere locally away from p.
I will end with two applications. Firstly, I will show how to construct counterexamples to Hasse’s principle of the shape X_E^-(p) for fixed E and infinitely many primes p. Secondly, I will present an application of the modular method together with our results to prove certain generalized Fermat equations have no non-trivial coprime solutions.
