  We prove a purely local form of a result of Saito and Yatagawa. They proved
that the characteristic cycle of a constructible \'etale sheaf is determined by
wild ramification of the sheaf along the boundary of a compactification. But
they had to consider ramification at all the points of the compactification. We
give a pointwise result, that is, we prove that the characteristic cycle of a
constructible \'etale sheaf around a point is determined by wild ramification
at the point. The key ingredient is to prove that wild ramification of the
stalk of the nearby cycle complex of a constructible \'etale sheaf at a point
is determined by wild ramification at the point.
