%0 Journal Article
%T Connectedness of Kisin varieties for GL_2
%A Eugen Hellmann
%J Mathematics
%D 2010
%I arXiv
%X We show that the Kisin varieties associated to simple $\phi$-modules of rank $2$ are connected in the case of an arbitrary cocharacter. This proves that the connected components of the generic fiber of the flat deformation ring of an irreducible $2$-dimensional Galois representation of a local field are precisely the components where the multiplicities of the Hodge-Tate weights are fixed.
%U http://arxiv.org/abs/1008.3071v1