Compact approximation and descent for algebraic stacks
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908343701864448 |
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| author | Hall, Jack Lamarche, Alicia Lank, Pat Peng, Fei |
| author_facet | Hall, Jack Lamarche, Alicia Lank, Pat Peng, Fei |
| contents | This work focuses on approximation and generation for the derived category of complexes with quasi-coherent cohomology on algebraic stacks. Our methods establish that approximation by compact objects descends along covers that are quasi-finite and flat. This generalizes a result of Lipman--Neeman for schemes and extends a related result known for algebraic spaces. We also study the behavior of generation under the derived pushforward and pullback of a morphism between algebraic stacks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compact approximation and descent for algebraic stacks Hall, Jack Lamarche, Alicia Lank, Pat Peng, Fei Algebraic Geometry 14A30 (primary), 18F20, 14F08, 18G80 This work focuses on approximation and generation for the derived category of complexes with quasi-coherent cohomology on algebraic stacks. Our methods establish that approximation by compact objects descends along covers that are quasi-finite and flat. This generalizes a result of Lipman--Neeman for schemes and extends a related result known for algebraic spaces. We also study the behavior of generation under the derived pushforward and pullback of a morphism between algebraic stacks. |
| title | Compact approximation and descent for algebraic stacks |
| topic | Algebraic Geometry 14A30 (primary), 18F20, 14F08, 18G80 |
| url | https://arxiv.org/abs/2504.21125 |