On unitary deformations of smooth modular representations

摘要

Let G be a lo/cally ℚ p -analytic group and K a finite extension of ℚ p with residue field k. Adapting a strategy of B. Mazur (cf. [Maz89]) we use deformation theory to study the possible liftings of a given smooth G-representation ρ over k to unitary G-Banach space representations over K. The main result proves the existence of a universal deformation space in case ρ admits only scalar endomorphisms. As an application we let G = GL2(ℚ p ) and compute the fibers of the reduction map in principal series representations.