  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.
