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 …

RECONSTRUCTING SCHEMES FROM THE DERIVED CATEGORY Page 1 Proceedings of
the Edinburgh Mathematical Society (2012) 55, 781–796 DOI:10.1017/S0013091510000076 …

A theorem of Bondal and Orlov states that a smooth projective variety with ample or anti-
ample canonical bundle can be reconstructed from its derived category. Here we extend the …

These notes aim to complement the lecture notes of Caldararu by providing an introduction
to explicit methods in the study of derived categories in algebraic geometry. The bounded …

For a noetherian scheme that has an ample family of invertible sheaves, we prove that direct
products in the category of quasi-coherent sheaves are not exact unless the scheme is …

Abstract We study Gorenstein categories. We show that such a category has Tate
cohomological functors and Avramov–Martsinkovsky exact sequences connecting the …

arXiv:0905.3148v2 [math.AG] 21 Sep 2009 Page 1 arXiv:0905.3148v2 [math.AG] 21 Sep 2009
EQUIVALENCES OF DERIVED CATEGORIES OF SHEAVES ON QUASI-PROJECTIVE …

We examine the localizing subcategories of the derived category of quasi-coherent sheaves
on the projective line over a field. We provide a complete classification of all such …

We study the following generalization of singularity categories. Let X be a quasi-projective
Gorenstein scheme with isolated singularities and A a non-commutative resolution of …

For an exact category having enough projective objects, we establish a bijection between
thick subcategories containing the projective objects and thick subcategories of the stable …