Semi-Bousfield classes generalize Bousfield classes and tensor-compatible t-structures, with a bijection assigning (nonmonotone) perversities on Noetherian schemes X to semi-Bousfield classes in D_qc(X) that stratifies the full lattice when X is regular.
Classification and nonexistence for $t$-structures on derived categories of schemes
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Given a suitable Noetherian scheme, we classify tensor $t$-structures on the bounded derived category of coherent sheaves and its variants with prescribed support. Furthermore, we show that the existence of such $t$-structures restricting to perfect complexes detects regularity, recovering a theorem of Neeman in the affine case by different methods. Our tools establish local-to-global principles for tensor $t$-structures.
years
2026 2representative citing papers
A Noetherian scheme is locally a complete intersection iff every object of D^b_coh(X) is t-⊗-proxy small, with classifications of ⊗-suspended subcategories for hypersurface and complete-intersection cases.
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Semi-Bousfield classes and nonmonotone perversities
Semi-Bousfield classes generalize Bousfield classes and tensor-compatible t-structures, with a bijection assigning (nonmonotone) perversities on Noetherian schemes X to semi-Bousfield classes in D_qc(X) that stratifies the full lattice when X is regular.
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Proxy smallness meets $t$-structures
A Noetherian scheme is locally a complete intersection iff every object of D^b_coh(X) is t-⊗-proxy small, with classifications of ⊗-suspended subcategories for hypersurface and complete-intersection cases.