Mod p Langlands correspondence for GL2 and Gelfand-Kirillov dimension — Yitong Wang (Université Paris-Saclay)

The mod p Langlands correspondence is completely known for the group GL2(Qp) by the work of Breuil, Colmez, etc. However, the situation becomes much more difficult when we replace Qp with a nontrivial finite extension. By a result of Emerton, the mod p Langlands correspondence for GL2(Qp) can be realized in the cohomology of modular curves, thus it is natural to look for a hypothetical correspondence for GL2 in the cohomology of Shimura curves. In this talk, I will compute the Gelfand-Kirillov dimensions of the representations of GL2 coming from the cohomology of Shimura curves. This builds on and extends the work of Breuil-Herzig-Hu-Morra-Schraen.