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Transactions of the American Mathematical Society

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The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Characteristic class and the $\varepsilon$-factor of an étale sheaf
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by Naoya Umezaki, Enlin Yang and Yigeng Zhao PDF
Trans. Amer. Math. Soc. 373 (2020), 6887-6927 Request permission


We prove a twist formula for the $\varepsilon$-factor of a constructible sheaf on a projective smooth variety over a finite field in terms of characteristic class of the sheaf. This formula is a modified version of the formula conjectured by Kato and Saito in [Ann. of Math. 168 (2008), pp. 33–96].

We give two applications of the twist formula. First, we prove that the characteristic classes of constructible étale sheaves on projective smooth varieties over a finite field are compatible with proper push-forward. Secondly, we show that the two Swan classes in the literature are the same on proper smooth surfaces over a finite field.

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Additional Information
  • Naoya Umezaki
  • Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
  • MR Author ID: 1171997
  • Email:,
  • Enlin Yang
  • Affiliation: School of Mathematical Sciences, Peking University, No.5 Yiheyuan Road Haidian District., Beijing, 100871, People’s Republic of China
  • Email:,
  • Yigeng Zhao
  • Affiliation: School of Sciences, Westlake University, 310024 Hangzhou, People’s Republic of China; and Institute of Sciences, Westlake Institute for Advanced Study, 310024 Hangzhou, People’s Republic of China
  • MR Author ID: 1278775
  • Email:,
  • Received by editor(s): November 7, 2018
  • Received by editor(s) in revised form: June 14, 2019, and September 5, 2019
  • Published electronically: August 6, 2020
  • Additional Notes: Enlin Yang is the corresponding author.
    The second author was partially supported by NSFC grants 11901008, and Alexander von Humboldt Foundation for his research at Universität Regensburg and Freie Universität Berlin.
    Both the second and the third authors were partially supported by the DFG through CRC 1085 Higher Invariants (Universität Regensburg). The authors are grateful to these institutions.
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 6887-6927
  • MSC (2010): Primary 14F20; Secondary 11G25, 11S40
  • DOI:
  • MathSciNet review: 4155195