Generalising Deligne and Deligne-Serre's results in the elliptic modular case, Carayol, Taylor and Jarvis have explained how to construct Galois representations from cuspidal Hilbert modular eigenforms. In particular, Jarvis used congruences to construct these representations in the `low weight' cases (where some of the weights are equal to 1). Whenever one has a global Galois representation associated to an automorphic representation (e.g. the automorphic representation generated by a modular eigenform) one expects to recover the local Langlands correspondence when comparing the local Galois representations obtained by restricting to decomposition subgroups with the local factors of the automorphic representation - this statement is known as `local-global compatibility'. Jarvis already proved most cases of local-global compatibility for low weight Hilbert modular forms, but a few cases remain unknown. I will discuss an approach to proving local-global compatibility in these remaining cases, using tools from the p-adic Langlands programme (in particular, Emerton's completed cohomology and a generalisation, due to Kassaei, of Buzzard and Taylor's results on analytic continuation of overconvergent eigenforms).
Freitag, den 10. Januar 2014 um 13:30 Uhr, in INF 288, HS2 Freitag, den 10. Januar 2014 at 13:30, in INF 288, HS2
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. G. Böckle