Characteristic cycles and the conductor of direct image
Algebraic Geometry
2021-01-05 v4
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.
Keywords
Cite
@article{arxiv.1704.04832,
title = {Characteristic cycles and the conductor of direct image},
author = {Takeshi Saito},
journal= {arXiv preprint arXiv:1704.04832},
year = {2021}
}
Comments
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