Six-Functor Formalisms III: The construction and extension of 6FFs
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915129510068224 |
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| author | Chowdhury, Chirantan |
| author_facet | Chowdhury, Chirantan |
| contents | This article is the last of the series of articles where we reprove the foundational ideas of abstract six-functor formalisms developed by Liu-Zheng. We prove the theorem of partial adjoints, which is a simplicial technique of encoding various functors altogether by taking adjoints along specific directions. Combined with the $\infty$-categorical compactification theorem from the previous article, we can construct abstract six-functor formalisms in reasonable geometric setups of our interest. We also reprove the simplified versions of the DESCENT program due to Liu-Zheng, which allows us to extend such formalisms from smaller to larger geometric setups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20548 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Six-Functor Formalisms III: The construction and extension of 6FFs Chowdhury, Chirantan Algebraic Geometry K-Theory and Homology This article is the last of the series of articles where we reprove the foundational ideas of abstract six-functor formalisms developed by Liu-Zheng. We prove the theorem of partial adjoints, which is a simplicial technique of encoding various functors altogether by taking adjoints along specific directions. Combined with the $\infty$-categorical compactification theorem from the previous article, we can construct abstract six-functor formalisms in reasonable geometric setups of our interest. We also reprove the simplified versions of the DESCENT program due to Liu-Zheng, which allows us to extend such formalisms from smaller to larger geometric setups. |
| title | Six-Functor Formalisms III: The construction and extension of 6FFs |
| topic | Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2412.20548 |