  In this paper, we study deformations of pairs (C,G) where G is a height 2
BT(or BT_n) group over a complete curve on algebraically closed field k of
characteristic p. We prove that, if the curve C is a versal deformation of G,
then there exists a unique lifting of the pair to the Witt ring W. We apply
this result in the case of Shimura curves to obtain a lifting criterion.
