Resolutions of singularities and triangulated categories

Peter Jørgensen

Bondal and Orlov’s categorical desingularization amounts to writing D^{b}(X) as a quotient of T^{c}, where D^{b}(X) is the derived category of bounded complexes of coherent sheaves on the space X, while T^{c} is the subcategory of compact objects in the triangulated category T. I will demonstrate a naive trick which enables me to find a T with T^{c} = D^{b}(Y) when X is sufficiently nice. There’s also a more general result which comes at the cost of allowing a more general T.