Vol. 3, No. 2, 2018

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

Johannes Schmidt and Florian Strunk

Vol. 3 (2018), No. 2, 331–367

We show that A1-localization decreases the stable connectivity by at most one over a Dedekind scheme with infinite residue fields. For the proof, we establish a version of Gabber’s geometric presentation lemma over a henselian discrete valuation ring with infinite residue field.

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$\mathbb{A}^1$-homotopy theory, motivic homotopy theory
Mathematical Subject Classification 2010
Primary: 14F42
Secondary: 55P42
Received: 19 December 2016
Revised: 4 April 2017
Accepted: 19 April 2017
Published: 24 March 2018
Johannes Schmidt
Mathematisches Institut
Ruprecht-Karls-Universität Heidelberg
Florian Strunk
Fakultät für Mathematik
Universität Regensburg