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arXiv · 2308.03155

Applications of perverse sheaves in commutative algebra

Bhargav Bhatt·Manuel Blickle·Gennady Lyubeznik·Anurag K. Singh·Wenliang Zhang
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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.

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Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, Anurag K. Singh, Wenliang Zhang. 2023-08-06. Applications of perverse sheaves in commutative algebra. https://arxiv.org/abs/2308.03155

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