We extend Urban’s construction of eigenvarieties for reductive groups such that has discrete series to include characteristic points at the boundary of weight space. In order to perform this construction, we define a notion of “locally analytic” functions and distributions on a locally -analytic manifold taking values in a complete Tate -algebra in which is not necessarily invertible. Our definition agrees with the definition of locally analytic distributions on -adic Lie groups given by Johansson and Newton.
"Equidimensional adic eigenvarieties for groups with discrete series." Algebra Number Theory 13 (8) 1907 - 1940, 2019. https://doi.org/10.2140/ant.2019.13.1907