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Perverse coherent sheaves (after Deligne)

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abstract

This note is mostly an exposition of an unpublished result of Deligne, which introduces an analogue of perverse $t$-structure on the derived category of coherent sheaves on a Noetherian scheme with a dualizing complex. Construction extends to the category of coherent sheaves equivariant under an action of an algebraic group; though proof of the general statement in this case does not require new ideas, it provides examples (such as sheaves on the nilpotent cone of a semi-simple group equivariant under the adjoint action) where construction of coherent "intersection cohomology" sheaves works.

fields

math.CT 1

years

2026 1

verdicts

UNVERDICTED 1

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Semi-Bousfield classes and nonmonotone perversities

math.CT · 2026-05-28 · unverdicted · novelty 7.0

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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  • Semi-Bousfield classes and nonmonotone perversities math.CT · 2026-05-28 · unverdicted · none · ref 3 · internal anchor

    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.