Annals of K-Theory

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

Johannes Schmidt and Florian Strunk

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We show that A 1 -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.

Article information

Ann. K-Theory, Volume 3, Number 2 (2018), 331-367.

Received: 19 December 2016
Revised: 4 April 2017
Accepted: 19 April 2017
First available in Project Euclid: 4 April 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14F42: Motivic cohomology; motivic homotopy theory [See also 19E15]
Secondary: 55P42: Stable homotopy theory, spectra

$\mathbb{A}^1$-homotopy theory motivic homotopy theory


Schmidt, Johannes; Strunk, Florian. Stable $\mathbb{A}^1$-connectivity over Dedekind schemes. Ann. K-Theory 3 (2018), no. 2, 331--367. doi:10.2140/akt.2018.3.331.

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