Measuring rationality of Schwede--Takagi pairs

We begin by giving a derived characterization of rational singularities for pairs in the sense of Schwede–Takagi. This characterization extends a characterization of rational singularities due to Lank–Venkatesh to pairs on normal varieties over fields of characteristic zero. As an application, we introduce a categorical invariant that measures the failure of rationality for pairs on affine varieties that are locally complete intersections.