Tensor t-structures on D^b_coh(X) and variants for suitable Noetherian schemes X are classified, with existence on perfect complexes detecting regularity and local-to-global principles established.
Measuring rationality of Schwede--Takagi pairs
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abstract
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.
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2024 1verdicts
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Classification and nonexistence for $t$-structures on derived categories of schemes
Tensor t-structures on D^b_coh(X) and variants for suitable Noetherian schemes X are classified, with existence on perfect complexes detecting regularity and local-to-global principles established.