Seminario de Teoría de Números

Title: Inertia Types of Elliptic Curves over Qp²

SPEAKER: Jose Antonio Castro Moreno (ICMAT)

DATE & TIME: Jueves 18 de septiembre - 11:30

VENUE: Aula 420, Departamento de Matemáticas, UAM.

ABSTRACT: Associated with an elliptic curve E defined over a finite  
extension K of Qp one can define the WeilDeligne representation ρ :  
W(K/K) → GL2(C). The isomorphism class of ρ restricted to the inertia  
subgroup is called the inertial type of E. These inertial types play  
an important role in several
topics that range from Diophantine applications to a proposed  
generalization of Maeda’s conjecture by Dieulefait, Pacetti and  
Tsaknias. In a recent work, Dembélé-Freitas-Voight provided a complete  
classification and explicit description of all the possible inertial  
types for elliptic curves defined over Qp for all p. In this talk we  
will present a complete classification and description of the inertial  
types over quadratic unramified extension of Qp. This is joint work  
with Nuno Freitas.