On the structure of some moduli spaces of finite flat group schemes

We consider the moduli space, in the sense of Kisin, of finite flat models of a 2-dimensional representation with values in a finite field of the absolute Galois group of a totally ramified extension of $\mathbb Q_p$. We determine the connected components of this space and describe its irreducible components in the case of an irreducible Galois representation. These results prove a modified version of a conjecture of Kisin.