  We propose the notion of the {\em crystalline sub-representation functor}
defined on $p$-adic representations of the Galois groups of finite extensions
of $\Qp$, with certain restrictions in the case of integral representations. By
studying its right-derived functors, we find a natural extension of a formula
of Grothendieck expressing the group of connected components of a Neron model
of an abelian variety in terms of Galois cohomology.
