Characteristic cycles and the conductor of direct image

Saito, Takeshi

doi:10.1090/jams/959

Characteristic cycles and the conductor of direct image
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by Takeshi Saito

J. Amer. Math. Soc. 34 (2021), 369-410

DOI: https://doi.org/10.1090/jams/959

Published electronically: December 2, 2020

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Abstract:

We prove the functoriality for a 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.

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