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Relative singular support and the semi-continuity of characteristic cycles for étale sheaves

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Abstract

Recently, the singular support and the characteristic cycle of an étale sheaf on a smooth variety over a perfect field are constructed by Beilinson and Saito, respectively. In this article, we extend the singular support to a relative situation. As an application, we prove the generic constancy for singular supports and characteristic cycles of étale sheaves on a smooth fibration. Meanwhile, we show the failure of the lower semi-continuity of characteristic cycles in a higher relative dimension case, which is different from Deligne and Laumon’s result in the relative curve case.

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Haoyu Hu

  2. Fakultät für Mathematik, Universität Regensburg, 93040, Regensburg, Germany

    Enlin Yang

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  1. Haoyu Hu
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  2. Enlin Yang
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Correspondence to Enlin Yang.

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Hu, H., Yang, E. Relative singular support and the semi-continuity of characteristic cycles for étale sheaves. Sel. Math. New Ser. 24, 2235–2273 (2018). https://doi.org/10.1007/s00029-017-0355-1

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