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

• Haoyu Hu ^[1] ; Enlin Yang ^[2]
  1. [1] University of Tokyo

     University of Tokyo

     Japón

     
  2. [2] University of Regensburg

     University of Regensburg

     Kreisfreie Stadt Regensburg, Alemania

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 3, 2018, págs. 2235-2273
• Idioma: inglés
• Enlaces
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• Resumen

  • 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.