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arXiv · 1602.08356

Stable $\mathbb{A}^1$-connectivity over Dedekind schemes

Johannes Schmidt·Florian Strunk
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Abstract

We show that $\mathbb{A}^1$-localization decreases the Nisnevich-stalkwise connectivity by at most one over a Dedekind scheme with infinite residue fields. For the proof, we establish a Nisnevich-local version of Gabber's geometric presentation lemma over a henselian discrete valuation ring with infinite residue field.

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Johannes Schmidt, Florian Strunk. 2016-02-26. Stable $\mathbb{A}^1$-connectivity over Dedekind schemes. https://doi.org/10.2140/akt.2018.3.331

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