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 $l \neq p$,
and explain how it can be proved with global methods.
Tuesday March 14, 2017 at 11:00 AM in SEO 612