Jack Shotton : The Breuil-Mézard conjecture when $l \ne p$

Posted by Ramin Takloo-Bighash , part of the Number Theory Seminar.

At

March 14, 2017, 11 a.m.

In

SEO 612

Abstract

Let $G = {\rm Gal}\,(\overline{\mathbb Q}_p/\mathbb Q_p)$. The Breuil-Mézard conjecture relates the complexity of deformation rings for mod $p$ Galois representations of $G$ with prescribed $p$-adic Hodge type to the reduction mod $p$ of representations of $GL_n(\mathbb Z_p)$ associated to that type. It has been important in the $p$-adic Langlands program and in first proof of the Fontaine-Mazur conjecture for $GL_2$. We develop an analogous conjecture for mod $l$ representations of $G$ when $l \neq p$, and explain how it can be proved with global methods.