We prove a purely local form of a result of Saito and Yatagawa. They proved that the characteristic cycle of a constructible étale 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 étale sheaf around a point is determined by wild ramification at that point. The key ingredient is to prove that wild ramification of the stalk of the nearby cycle complex of a constructible étale sheaf at a point is determined by wild ramification at that point.

我们证明了 Saito 和 Yatagawa 结果的纯局部形式。他们证明了可构造的 étale 层的特征循环是由层沿压实边界的野生分枝决定的。但是他们必须在紧凑化的所有点上考虑分枝。我们给出了一个逐点结果，即我们证明了围绕一个点的可构造 étale 层的特征循环是由该点的野生分支决定的。关键要素是证明可构造的 étale 束的附近循环复合体的茎在某一点的野生分支是由该点的野生分支决定的。