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$\mathbb {A}^1$
-CONNECTIVITY OF MOTIVIC SPACES
- Part of
-
- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 25 / Issue 5 / September 2026
- Published online by Cambridge University Press:
- 15 July 2026, pp. 2961-2971
- Print publication:
- September 2026
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- Article
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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.
