Non-representable six-functor formalisms
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916569643220992 |
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| author | Chowdhury, Chirantan D'Angelo, Alessandro |
| author_facet | Chowdhury, Chirantan D'Angelo, Alessandro |
| contents | In this article, we study the properties of motivic homotopy category $\mathcal{SH}_{\operatorname{ext}}(\mathcal{X})$ developed by Chowdhury and Khan-Ravi for $\mathcal{X}$ a Nis-loc Stack. In particular, we compare the above construction with Voevodsky's original construction using NisLoc topology. Using the techniques developed by Liu-Zheng and Mann's notion of $\infty$-category of correspondences and abstract six-functor formalisms, we also extend the exceptional functors and extend properties like projection formula, base change and purity to the non-representable situation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20382 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-representable six-functor formalisms Chowdhury, Chirantan D'Angelo, Alessandro Algebraic Geometry K-Theory and Homology In this article, we study the properties of motivic homotopy category $\mathcal{SH}_{\operatorname{ext}}(\mathcal{X})$ developed by Chowdhury and Khan-Ravi for $\mathcal{X}$ a Nis-loc Stack. In particular, we compare the above construction with Voevodsky's original construction using NisLoc topology. Using the techniques developed by Liu-Zheng and Mann's notion of $\infty$-category of correspondences and abstract six-functor formalisms, we also extend the exceptional functors and extend properties like projection formula, base change and purity to the non-representable situation. |
| title | Non-representable six-functor formalisms |
| topic | Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2409.20382 |