Conjectures and Results on Modular Representations of $\mathrm{GL}_n(K)$ for a $p$-Adic Field $K$

Christophe Breuil, Faculte d'Orsay, Universite Paris-Saclay, France Florian Herzig, University of Toronto, Ontario, Canada. Yongquan Hu, Morningside Center of Mathematics, No. 55, Beijing, People's Republic of China. Stefano Morra, Laboratoire d'Analyse, Geometrie et Applications, Universite Sorbonne Paris Nord, Villetaneuse, France. Benjamin Schraen, Faculte d'Orsay, Universite Paris-Saclay, France

• Chapters; 1. Introduction; 2. Local-global compatibility conjectures; 3. The case of \texorpdfstring{ GL_2(\mathbb {Q}_{p^f})}GL_2(Q_{p^f})