Dualizing complexes and perverse sheaves on noncommutative ringed schemes

• Amnon Yekutieli ^[2] ; James J. Zhang ^[1]
  1. [1] University of Washington

     University of Washington

     Estados Unidos

     
  2. [2] Ben-Gurion University of the Negev

     Ben-Gurion University of the Negev

     Israel

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 12, Nº. 1, 2006, págs. 137-177
• Idioma: inglés
• DOI: 10.1007/s00029-006-0022-4
• Enlaces
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• Resumen

  • A quasi-coherent ringed scheme is a pair (X, A), where X is a scheme, and A is a noncommutative quasi-coherent OX-ring. We introduce dualizing complexes over quasi-coherent ringed schemes and study their properties.

    For a separated differential quasi-coherent ringed scheme of finite type over a field, we prove existence and uniqueness of a rigid dualizing complex.

    In the proof we use the theory of perverse coherent sheaves in order to glue local pieces of the rigid dualizing complex into a global complex.