Perverse pullbacks
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918163716767744 |
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| author | Khan, Adeel A. Kinjo, Tasuki Park, Hyeonjun Safronov, Pavel |
| author_facet | Khan, Adeel A. Kinjo, Tasuki Park, Hyeonjun Safronov, Pavel |
| contents | We define a new perverse t-exact pullback operation on derived categories of constructible sheaves which generalizes most perverse t-exact functors in sheaf theory, such as microlocalization, the Fourier-Sato transform and vanishing cycles. This operation is defined for morphisms of algebraic stacks equipped with a relative exact (-1)-shifted symplectic structure, and can be used to define cohomological Donaldson-Thomas invariants in a relative setting. We prove natural functoriality properties for perverse pullbacks, such as smooth and finite base change, compatibility with products and Verdier duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16563 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Perverse pullbacks Khan, Adeel A. Kinjo, Tasuki Park, Hyeonjun Safronov, Pavel Algebraic Geometry We define a new perverse t-exact pullback operation on derived categories of constructible sheaves which generalizes most perverse t-exact functors in sheaf theory, such as microlocalization, the Fourier-Sato transform and vanishing cycles. This operation is defined for morphisms of algebraic stacks equipped with a relative exact (-1)-shifted symplectic structure, and can be used to define cohomological Donaldson-Thomas invariants in a relative setting. We prove natural functoriality properties for perverse pullbacks, such as smooth and finite base change, compatibility with products and Verdier duality. |
| title | Perverse pullbacks |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2510.16563 |