The Breuil–Mezard conjecture over function fields

Seminar: 
Algebra and Number Theory Seminar
Event time: 
Tuesday, November 19, 2019 - 4:15pm
Location: 
LOM 205
Speaker: 
Zijian Yao
Speaker affiliation: 
Harvard University
Event description: 

Abstract: We describe a Breuil–Mezard type conjecture that relates structure of mod l fibers of deformation rings of the Galois group of a local field K (which has residue characteristic p different from l) to deformations of smooth mod l representations of GL_n(K). These conjectures are centered around the compatibility between inertial local Langlands and its mod l version. We sketch a proof of a weaker version of the conjecture, when K is a local function field, using the Taylor–Wiles–Kisin patching method. If time permits, we will report on some progress on variants for the conjecture for inner forms.