Integral transforms on singularity categories for Noetherian schemes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918140893462528 |
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| author | Dutta, Uttaran Lank, Pat Rahul, Kabeer Manali |
| author_facet | Dutta, Uttaran Lank, Pat Rahul, Kabeer Manali |
| contents | This work studies conditions under which integral transforms induce exact functors on singularity categories between schemes that are proper over a Noetherian base scheme. A complete characterization for this behavior is provided, which extends earlier work of Ballard and Rizzardo. We leverage a description of the bounded derived category of coherent sheaves as finite cohomological functors on the category of perfect complexes, which is an application of Neeman's approximable triangulated categories, to reduce arguments to an affine local setting. Moreover, we study adjoints of such functors, extend a result of Olander to varieties with mild singularities, and provide an obstruction for derived equivalences between singular varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13834 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integral transforms on singularity categories for Noetherian schemes Dutta, Uttaran Lank, Pat Rahul, Kabeer Manali Algebraic Geometry Commutative Algebra 14A30 (primary), 14F08, 18G80, 14B05 This work studies conditions under which integral transforms induce exact functors on singularity categories between schemes that are proper over a Noetherian base scheme. A complete characterization for this behavior is provided, which extends earlier work of Ballard and Rizzardo. We leverage a description of the bounded derived category of coherent sheaves as finite cohomological functors on the category of perfect complexes, which is an application of Neeman's approximable triangulated categories, to reduce arguments to an affine local setting. Moreover, we study adjoints of such functors, extend a result of Olander to varieties with mild singularities, and provide an obstruction for derived equivalences between singular varieties. |
| title | Integral transforms on singularity categories for Noetherian schemes |
| topic | Algebraic Geometry Commutative Algebra 14A30 (primary), 14F08, 18G80, 14B05 |
| url | https://arxiv.org/abs/2501.13834 |