A01 Automorphic forms and the p-adic Langlands programme

The past years have seen tremendous progress in the development of a categorical approach to the arithmetic of the Langlands programme. In the context of the p-adic Langlands programme the main features of this approach are the study of derived categories of p-adic representations of p-adic Lie groups, the study of (coherent) sheaves on moduli of Galois representations associated to such representations, and the development of a more geometric approach to such representations. The project addresses all these three aspects of the programme.