Kisin, Mark2011-04-042010Kisin, Mark. 2010. Deformations of GQp and GL2(Qp) Representations. Astérisque 330: 511-528.97828562928150303-1179http://nrs.harvard.edu/urn-3:HUL.InstRepos:4794887We show that Colmez's functor from GL2(Qp) representations to GQp representation produces essentially all two dimensional representations of GQp. The method compares the deformation theory for the two kinds of representations: An group calculation of Colmez implies that the deformation space for GL2(Qp) representations is closed in that for GQp-representations. A local version of the Gouvêa-Mazur "infinite fern'' argument shows that this closed subspace is also dense.en-USgalois representationdeformationJournal Article2011-04-04