  For a curve $X$ over a $p$-adic field $k$, using the class field theory of
$X$ due to S. Bloch and S. Saito we study the abelian geometric fundamental
group $\pi_1^{\mathrm{ab}}(X)^{\mathrm{geo}}$ of $X$. In particular, it is
investigated a subgroup of $\pi_1^{\mathrm{ab}}(X)^{\mathrm{geo}}$ which
classifies the geometric and abelian coverings of $X$ which allow possible
ramification over the special fiber of the model of $X$. Under the assumptions
that $X$ has a $k$-rational point, $X$ has good reduction and its Jacobian
variety has good ordinary reduction, we give some upper and lower bounds of
this subgroup of $\pi_1^{\mathrm{ab}}(X)^{\mathrm{geo}}$.
