Applications of perverse sheaves in commutative algebra
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
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| _version_ | 1866913755076493312 |
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| author | Bhatt, Bhargav Blickle, Manuel Lyubeznik, Gennady Singh, Anurag K. Zhang, Wenliang |
| author_facet | Bhatt, Bhargav Blickle, Manuel Lyubeznik, Gennady Singh, Anurag K. Zhang, Wenliang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_03155 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Applications of perverse sheaves in commutative algebra Bhatt, Bhargav Blickle, Manuel Lyubeznik, Gennady Singh, Anurag K. Zhang, Wenliang Algebraic Geometry Commutative Algebra 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. |
| title | Applications of perverse sheaves in commutative algebra |
| topic | Algebraic Geometry Commutative Algebra |
| url | https://arxiv.org/abs/2308.03155 |