nLab categorical resolution of singularities

Definition

Given a dg-algebra $B$ a categorical resolution of the derived category $D(B)$ of $B$-modules is a pair $(A,X)$ of a dg-algebra $A$ and a dg-$B^{op}\otimes A$-module $X$ such that the restriction of the left derived functor

$$(-)\stackrel{L}\otimes_B X : D(B)\to D(A)$$

to the subcategory $Perf(B)$ of perfect complexes is full and faithful.

Literature

It is introduced in

• Valery Lunts, Categorical resolution of singularities, J. Algebra 323:10 (2010) 2977-3003 doi math.AG/0905.4566
• Alexander Kuznetsov, V. Lunts, Categorical resolutions of irrational singularities, arXiv:1212.6170
• Alexander I. Efimov, Homotopy finiteness of some DG categories from algebraic geometry, arXiv:1308.0135

category: algebraic geometry