Dualizing Complexes and Perverse Sheaves on Noncommutative Ringed Schemes

Details Dualizing Complexes and Perverse Sheaves on Noncommutative Ringed Schemes Dualizing Complexes and Perverse Sheaves on Noncommutative Ringed Schemes

2002-11-20

arxiv.org/abs/math/0211309v4

Mathematics

Algebraic Geometry

36 pages, AMSLaTeX. Final version, to appear in Selecta Math. (minor changes)

Scientific paper

A quasi-coherent ringed scheme is a pair (X,A), where X is a scheme, and A is a noncommutative quasi-coherent 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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