Derived categories of sheaves on singular schemes with an application to reconstruction

Details Derived categories of sheaves on singular schemes with an application to reconstruction Derived categories of sheaves on singular schemes with an application to reconstruction

2008-01-17

arxiv.org/abs/0801.2599v3

Advances in Mathematics, Volume 227, Issue 2, 1 June 2011, Pages 895-919

Mathematics

Algebraic Geometry

23 pages. Final version although comments and suggestions are always welcome

Scientific paper

We prove that the bounded derived category of coherent sheaves with proper support is equivalent to the category of locally-finite, cohomological functors on the perfect derived category of a quasi-projective scheme over a field. We introduce the notions of pseudo-adjoints and Rouquier functors and study them. As an application of these ideas and results, we extend the reconstruction result of Bondal and Orlov to Gorenstein projective varieties.

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