Meeting ID:  920 2195 5230

Passcode:    The three-digit integer that is the cube of the sum of its digits.

The Fontaine-Mazur conjecture (proved by Kisin and Emerton) says that (under certain technical hypotheses) a Galois representation \rho:Gal_Q\rightarrow GL_2(\overline{Q}_p)$ is modular if it is unramified outside finitely many places and de Rham at p. I will talk about what this means, and I will discuss an analogous modularity result for Galois representations \rho:Gal_Q\rightarrow GL_2(L) when L is instead a non-archimedean local field of characteristic p.