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.
Perverse coherent sheaves.arXiv preprint, arXiv:0902.0349,
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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.