Number Theory Seminar
Jack Shotton
University of Chicago
The Breuil-Mézard conjecture when $l \ne p$
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 $l \ne p$, and explain how it can be proved with global methods.
Tuesday April 4, 2017 at 11:00 AM in SEO 612