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Connectedness of Kisin varieties for GL_2

Eugen Hellmann

Number 38
Author Eugen Hellmann
Project B08
Year 2010

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.

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