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Applications of perverse sheaves in commutative algebra
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abstract
The goal of this paper is to explain how basic properties of perverse sheaves sometimes translate via Riemann-Hilbert correspondences (in both characteristic $0$ and characteristic $p$) to highly non-trivial properties of singularities, especially their local cohomology. Along the way, we develop a theory of perverse $\mathbf{F}_p$-sheaves on varieties in characteristic $p$, expanding on previous work by various authors, and including a strong version of the Artin vanishing theorem.
Forward citations
Cited by 2 Pith papers
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A Grauert-Riemenschneider vanishing theorem for Witt canonical sheaves
Proper birational maps from smooth varieties have vanishing higher rational Witt top-forms; in low dimensions the integral Witt sheaves are annihilated by a fixed p-power, yielding Q_p-rationality of F-rational singularities.
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Duality between $W_n$-Cartier crystals and $\mathbb{Z}/p^n\mathbb{Z}$-perverse sheaves
For Noetherian F-finite semi-separated F_q-schemes, W_n-Cartier crystals are dual to constructible perverse sheaves with W_n(F_q) coefficients.
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