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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Characteristic cycles and the conductor of direct image
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by Takeshi Saito
J. Amer. Math. Soc. 34 (2021), 369-410
Published electronically: December 2, 2020


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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Bibliographic Information
  • Takeshi Saito
  • Affiliation: School of Mathematical Sciences, University of Tokyo, Tokyo 153-8914, Japan
  • MR Author ID: 236565
  • Email:
  • 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.
  • © Copyright 2020 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 34 (2021), 369-410
  • MSC (2010): Primary 14F20
  • DOI:
  • MathSciNet review: 4280863