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

作者：Ballard Matthew Robert^*

来源：Advances in Mathematics, 2011, 227(2): 895-919.

DOI：10.1016/j.aim.2011.02.016

• Algebraic geometry
• Derived categories
• Compactly-generated triangulated categories

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.

• 出版日期2011-6-1