A categorical approach to the (p-adic) Langlands program searches for a functor from categories of representations of groups such as G = GLn(F), F a finite extension of Qp, to coherent sheaves on stacks of L-parameters. These functors are also supposed to feature in a description of the étale cohomology of Shimura varieties in terms of coherent cohomology of spaces of Galois representations. In this talk we will focus on locally analytic representations of G and we are looking for the description (in terms of coherent sheaves and Galois representations) of the cohomology of Shimura varieties with coefficients in certain overconvergent p-adic coefficient systems (closely related to overconvergent p-adic automorphic forms).I will explain what this description looks like in the case of the modular curve and discuss geometric properties of the spaces of Galois representations involved.