Characteristic cycles and the conductor of direct image

Abstract

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.

41 pages. Proposition 2.3.3 is corrected in v2. New subsection 1.1 is added in v3 to correct the proof of Lemma 1.4.9

References in corpus (1)

• The characteristic cycle and the singular support of a constructible sheaf

Cited by in corpus (2)

• Cohomological Milnor formula and Saito's conjecture on characteristic classes
• Cohomological boundedness for flat bundles on surfaces and applications