Continuous representation theory of $p$-adic Lie groups

Abstract

In this paper we give an overview over the basic features of the continuous representation theory of p-adic Lie groups as it has emerged during the last five years. The main motivation for developing such a theory is a possible extension of the local Langlands program to p-adic Galois representations. This is still very much in its infancy. But in the last section we will describe a first approximation to an extended Langlands functoriality principle for crystalline Galois representations.