Posted in

Speaker:

Pedro João Lemos
Affiliation:

MPIM
Date:

Wed, 2018-01-31 16:30 - 17:30
Location:

MPIM Lecture Hall
Parent event:

Number theory lunch seminar Given a number field $K$, Serre's uniformity question asks whether there exists a

constant $C_K$ (depending only on $K$) such that if $E/K$ is an elliptic curve

without complex multiplication, then $\bar{\rho}_{E,p}$ is surjective for every

prime $p>C_K$. In this talk, building on previous work by Darmon and Merel,

I will show that Serre's uniformity question has a positive answer for the family

of elliptic curves defined over the rationals, without complex multiplication and

admitting a non-trivial cyclic isogeny. I will then present some more recent

work I have been conducting on other families of elliptic curves.

© MPI f. Mathematik, Bonn | Impressum & Datenschutz |