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The Euler numbers of ℓ-adic sheaves of rank 1 in positive characteristic

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ICM-90 Satellite Conference Proceedings

Abstract

One of the most important themes in ramification theory is the formula for the Euler characteristic of ℓ-adic sheaves. Although we have the Grothendieck-Ogg-Shafarevich formula [G] in one dimensional case, we don’t have a general formula in higher dimension even in the form of a conjecture. However for sheaves of rank 1, K.Kato formulated a conjecture in arbitrary dimension and actually proved it in dimension 2 in [K2]. In this paper, we will prove it in arbitrary dimension under a certain hypothesis, which is hoped to hold when the variety is sufficiently blowed up.

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References

  1. P. Deligne, G. Lustig, Representation of reductive groups over finite fields, Annals of Math. 103 (1976), 103–161.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Tokyo, Tokyo, 113, Japan

    Takeshi Saito

Authors
  1. Takeshi Saito
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Editor information

Editors and Affiliations

  1. College of General Education, Kyoto University, Yoshida-nihonmatsu, Sakyo-ku, Kyoto, 606, Japan

    Akira Fujiki

  2. Department of Mathematics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113, Japan

    Kazuya Kato  & Yujiro Kawamata  & 

  3. Department of Mathematics, Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo, 112, Japan

    Toshiyuki Katsura

  4. Department of Mathematics, Rikkyo University, Nishi-ikebukuro, Toshima-ku, Tokyo, 171, Japan

    Yoichi Miyaoka

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© 1991 Springer-Verlag Tokyo

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Saito, T. (1991). The Euler numbers of ℓ-adic sheaves of rank 1 in positive characteristic. In: Fujiki, A., Kato, K., Kawamata, Y., Katsura, T., Miyaoka, Y. (eds) ICM-90 Satellite Conference Proceedings. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68172-4_9

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  • DOI: https://doi.org/10.1007/978-4-431-68172-4_9

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-70086-9

  • Online ISBN: 978-4-431-68172-4

  • eBook Packages: Springer Book Archive

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