| Résume | I will discuss joint work with Matthew Emerton and David Savitt, proving conjectures of Breuil and Dembele. More precisely, we prove a multiplicity one result for the mod p cohomology of a Shimura curve at Iwahori level, and we show that certain apparently globally defined lattices in the cohomology of Shimura curves are determined by the corresponding local p-adic Galois representations. Our main tools are the geometric Breuil–Mezard philosophy, and a new and more functorial perspective on the Taylor–Wiles–Kisin patching method. |
