  We seek an appropriate definition for a Shimura curve of Hodge type in
positive characteristics via characterizing curves in positive characteristics
which are reduction of Shimura curve over $\mathbb{C}$. In this paper, we study
the liftablity of a curve in the moduli space of principally polarized abelian
varieties over $k, \text{char} k=p$. We show that in the generic ordinary case,
some tensor decomposition of the isocrystal associated to the family imply that
this curve can be lifted to a Shimura curve.
