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.
Cotorsion pairs and Tor-pairs over commutative Noetherian rings.arXiv preprint, arXiv:2411.04514,
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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.