16:00
On p-ordinary, mod p local Langlands correspondences
Abstract
The established mod p local Langlands correspondence is a representation of GL2(Qp) that is associated to a local Galois representation and that occurs in the cohomology of the modular curve. It is believed that more general correspondences occur but, as of yet, this remains open. Examples of these generalisations would be representations of GLn(Qp) that are associated to higher dimensional Galois representations and that occur in the cohomology of suitable arithmetic manifolds.
In this talk, I will discuss joint work with Shu Sasaki in which we construct a purely local framework for associating a mod p representation of GLn(Qp) to the data of a mod p Galois representation whose image lives in a Borel subgroup (a mod p, p-ordinary Galois representation). We will see how our construction is motivated by earlier work of Breuil and Herzig and why we hope to use our framework to generalise their mod p results to include non generic cases.