  In this paper we investigate a local to global principle for Galois
cohomology of number fields with coefficients in the Tate module of an abelian
variety. In \cite{bk13} G. Banaszak and the author obtained the sufficient
condition for the validity of the local to global principle for {\'e}tale
$K$-theory of a curve . This condition in fact has been established by means of
an analysis of the corresponding problem in the Galois cohomology. We show that
in some cases this result is the best possible i.e if this condition does not
hold we obtain counterexamples.
  We also give some examples of curves and their Jacobians. Finally, we prove
the dynamical version of the local to global principle for {\'e}tale $K$-theory
of a curve. The dynamical local to global principle for the groups of
Mordell-Weil type has recently been considered by S. Bara{\'n}czuk in
\cite{b17}. We show that all our results remain valid for Quillen $K$-theory of
${\cal X}$ if the Bass and Quillen-Lichtenbaum conjectures hold true for ${\cal
X}.$

K-Theory and Homology;Algebraic Geometry