$\mathbb{A}^1$-connectivity of motivic spaces
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914195273940992 |
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| author | Bouis, Tess Kundu, Arnab |
| author_facet | Bouis, Tess Kundu, Arnab |
| contents | We prove an unstable version of Morel's $\mathbb{A}^1$-connectivity theorem over arbitrary base schemes. In the stable setting, this recovers (and simplifies the proof of) the known connectivity bounds due to Morel, Schmidt--Strunk, Deshmukh--Hogadi--Kulkarni--Yadav, and Druzhinin, and extends them to possibly non-noetherian schemes. Using the recent work of Bachmann--Elmanto--Morrow, this also implies that the slice filtration on homotopy $K$-theory is convergent for qcqs schemes of finite valuative dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10712 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathbb{A}^1$-connectivity of motivic spaces Bouis, Tess Kundu, Arnab Algebraic Geometry Algebraic Topology K-Theory and Homology We prove an unstable version of Morel's $\mathbb{A}^1$-connectivity theorem over arbitrary base schemes. In the stable setting, this recovers (and simplifies the proof of) the known connectivity bounds due to Morel, Schmidt--Strunk, Deshmukh--Hogadi--Kulkarni--Yadav, and Druzhinin, and extends them to possibly non-noetherian schemes. Using the recent work of Bachmann--Elmanto--Morrow, this also implies that the slice filtration on homotopy $K$-theory is convergent for qcqs schemes of finite valuative dimension. |
| title | $\mathbb{A}^1$-connectivity of motivic spaces |
| topic | Algebraic Geometry Algebraic Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2512.10712 |