  Let $K$ be a complete discrete valuation field with ring of integers $\co_K$.
Let $X/K$ be a proper smooth curve and let $A/K$ denote its jacobian. Let $P$
and $Q$ belong to $X(K)$. The divisor $P - Q$ defines a $K$-rational point of
$A/K$. In this article, we study the reduction of $P - Q$ in the N\'eron model
${\cal A}_K/{\cal O}_K$ of $A/K$ in terms of the reductions of the points $P$
and $Q$ in a regular model $\cx/\co_K$ of $X/K$.
  The author introduced earlier two functorial filtrations of the prime-to-$p$
part of the group of component $\Phi_K$ of ${\cal A}_K/{\cal O}_K$. Filtrations
for the full group $\Phi_K$ were later introduced by Bosch and Xarles. Given
two points $P$ and $Q$ in $X(K)$, it is natural to wonder whether it is
possible to predict when the reduction of $P-Q$ in $\Phi_K$ belongs to one of
these functorial subgroups. We give in this paper a sufficient condition on the
special fiber of a model $\cx$ for the image of $P-Q$ in $\Phi_K$ to belong to
the subgroup $\Psi_{K,L}$. When this condition is satisfied, we are able to
provide a formula for the order of this image. We conjecture that the
sufficient condition alluded to above is also necessary and we provide evidence
in support of this conjecture. We also discuss cases where the image of $P-Q$
belongs to a functorial subgroup of $\Psi_{K,L}$, using a pairing associated to
$\Phi_K$.
