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Characteristic cycles and the conductor of direct image


Author: Takeshi Saito
Journal: J. Amer. Math. Soc. 34 (2021), 369-410
MSC (2010): Primary 14F20
DOI: https://doi.org/10.1090/jams/959
Published electronically: December 2, 2020
MathSciNet review: 4280863
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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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References
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Additional Information

Takeshi Saito
Affiliation: School of Mathematical Sciences, University of Tokyo, Tokyo 153-8914, Japan
MR Author ID: 236565
Email: t-saito@ms.u-tokyo.ac.jp

Received by editor(s): May 6, 2017
Received by editor(s) in revised form: May 14, 2019, October 21, 2019, and February 24, 2020
Published electronically: December 2, 2020
Additional Notes: The research was supported by JSPS Grants-in-Aid for Scientific Research (A) 26247002.
Article copyright: © Copyright 2020 American Mathematical Society