Our work begins by providing a derived characterization of rational singularities for pairs in the sense of Schwede--Takagi. This characterization both generalizes and independently obtains a result of Lank--Venkatesh in the special case of varieties with rational singularities. As an application, we introduce a categorical invariant that measures the failure of rationality for pairs on affine varieties which are locally complete intersections.
Categories: math.AG math.AC