Dualizing complexes and perverse sheaves on noncommutative ringed schemes |
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Authors: | Amnon Yekutieli and James J Zhang |
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Institution: | (1) Department of Mathematics, Ben Gurion University, Be’er Sheva, 84105, Israel;(2) Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, USA |
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Abstract: | A quasi-coherent ringed scheme is a pair (X,
$$ \mathcal{A} $$), where X is a scheme, and
$$ \mathcal{A} $$
is a noncomutative quasi-coherent
$$ \mathcal{O}_X $$
-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. |
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Keywords: | Primary 14A22 Secondary 14F05 14J32 16E30 16D90 18E30 |
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