Reflexivity and rigidity for complexes, II: Schemes

Details Reflexivity and rigidity for complexes, II: Schemes Reflexivity and rigidity for complexes, II: Schemes

2010-01-20

arxiv.org/abs/1001.3450v1

Mathematics

Algebraic Geometry

40 pages

Scientific paper

We prove basic facts about reflexivity in derived categories over noetherian schemes; and about related notions such as semidualizing complexes, invertible complexes, and Gorenstein-perfect maps. Also, we study a notion of rigidity with respect to semidualizing complexes, in particular, relative dualizing complexes for Gorenstein-perfect maps. Our results include theorems of Yekutieli and Zhang concerning rigid dualizing complexes on schemes. This work is a continuation of part I, which dealt with commutative rings.

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