| Résume | It is known - starting with the work of Coleman and Mazur on the eigencurve - that the dual space of (finite slope) overconvergent p-adic automorphic forms can be identified with the global section of a coherent sheaf on a rigid analytic variety, called an eigenvariety. In this talk I will give a conjectural Galois theoretic description of this coherent sheaf in terms of an envisioned categorical p-adic Langlands correspondence (that is inspired by ideas from the geometric Langlands program as well as from the Taylor-Wiles patching method). I will discuss some partial results in the case of
the modular curve. |
