Algèbres de Hecke quasi-ordinaires universelles

Let be a connected reductive group over whose adjoint group admits discrete series representations. In this article, we construct a p-adic interpolation of the set of spaces of topological automorphic forms and we study the required properties to construct p-adic families of Hecke eigensystems. We impose a nearly-ordinarity assumption at p and we work with a local system of regular weight. Assuming Leopoldt conjecture, in the case of a unitary group in three variables associated with a CM extension of a totally real field F, we thus get p-adic families in variables.