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Paper

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

Abstract

We prove an unstable version of Morel's -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 -theory is convergent for qcqs schemes of finite valuative dimension.