We prove the functoriality for proper push-forward of the characteristic cycles of constructible complexes by morphisms of smooth projective schemes over a perfect field, under the assumption that the direct image of the singular support has the dimension at most that of the target of the morphism. The functoriality is deduced from a conductor formula which is a special case for morphisms to curves. The conductor formula in the constant coefficient case gives the geometric case of a formula conjectured by Bloch.

中文翻译：

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特征周期和直接像的导体

我们证明了通过完美域上的光滑射影方案的态射适当推进可构造复形的特征圈的函子性，假设奇异支座的直接像的维数至多是态射目标的维数. 函式是从导体公式推导出来的，导体公式是态射到曲线的特例。常系数情况下的导体公式给出了布洛赫推测的公式的几何情况。