$\mathbb{A}^1$-invariance of localizing invariants
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913365975105536 |
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| author | Sosnilo, Vladimir |
| author_facet | Sosnilo, Vladimir |
| contents | Weibel proved that $p$-inverted K-theory is $\mathbb{A}^1$-invariant on $\mathbb{F}_p$-schemes and K-theory with $\mathbb{Z}/p$-coefficients is $\mathbb{A}^1$-invariant on $\mathbb{Z}[\frac{1}{p}]$-schemes. We extend this result to all finitary localizing invariants of small stable $\infty$-categories. Along the way we study the Frobenius and Verschiebung endofunctors defined by Tabuada and provide a categorical version of Stienstra's projection formula. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2211_05602 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | $\mathbb{A}^1$-invariance of localizing invariants Sosnilo, Vladimir K-Theory and Homology Weibel proved that $p$-inverted K-theory is $\mathbb{A}^1$-invariant on $\mathbb{F}_p$-schemes and K-theory with $\mathbb{Z}/p$-coefficients is $\mathbb{A}^1$-invariant on $\mathbb{Z}[\frac{1}{p}]$-schemes. We extend this result to all finitary localizing invariants of small stable $\infty$-categories. Along the way we study the Frobenius and Verschiebung endofunctors defined by Tabuada and provide a categorical version of Stienstra's projection formula. |
| title | $\mathbb{A}^1$-invariance of localizing invariants |
| topic | K-Theory and Homology |
| url | https://arxiv.org/abs/2211.05602 |