A construction of the full eigenvariety of a reductive group

Abstract: In this paper, we construct for arbitrary reductive group a full eigenvariety, which parameterizes all p-adic overconvergent cohomological eigenforms of the group in the sense of Ash–Stevens and Urban. We also see that the eigenvariety constructed by Eric Urban (2011) is the union of those irreducible components of codimension zero in the eigenvariety we constructed, therefore we can formulate Urbanʼs conjectures. [Copyright &y& Elsevier]