On the algebraizability of formal deformations in $K$-cohomology
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914731596447744 |
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| author | Mackall, Eoin |
| author_facet | Mackall, Eoin |
| contents | We show that algebraizability of the functors $R^1π_*\mathcal{K}^M_{2,X}$ and $R^2π_*\mathcal{K}^M_{2,X}$ is a stable birational invariant for smooth and proper varieties $π:X\rightarrow k$ defined over an algebraic extension $k$ of $\mathbb{Q}$. The same is true for the étale sheafifications of these functors as well.
To get these results we introduce a notion of relative $K$-homology for schemes of finite type over a finite dimensional, Noetherian, excellent base scheme over a field. We include this material in an appendix. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19008 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the algebraizability of formal deformations in $K$-cohomology Mackall, Eoin Algebraic Geometry K-Theory and Homology 14C35 We show that algebraizability of the functors $R^1π_*\mathcal{K}^M_{2,X}$ and $R^2π_*\mathcal{K}^M_{2,X}$ is a stable birational invariant for smooth and proper varieties $π:X\rightarrow k$ defined over an algebraic extension $k$ of $\mathbb{Q}$. The same is true for the étale sheafifications of these functors as well. To get these results we introduce a notion of relative $K$-homology for schemes of finite type over a finite dimensional, Noetherian, excellent base scheme over a field. We include this material in an appendix. |
| title | On the algebraizability of formal deformations in $K$-cohomology |
| topic | Algebraic Geometry K-Theory and Homology 14C35 |
| url | https://arxiv.org/abs/2403.19008 |