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arXiv · 2512.10712

$\mathbb{A}^1$-connectivity of motivic spaces

Tess Bouis·Arnab Kundu
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Abstract

We prove a version of Morel's unstable $\mathbb{A}^1$-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.

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Tess Bouis, Arnab Kundu. 2025-12-11. $\mathbb{A}^1$-connectivity of motivic spaces. https://arxiv.org/abs/2512.10712

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