## Annals of K-Theory

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

#### Abstract

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

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

Dates
Revised: 4 April 2017
Accepted: 19 April 2017
First available in Project Euclid: 4 April 2018

https://projecteuclid.org/euclid.akt/1522807265

Digital Object Identifier
doi:10.2140/akt.2018.3.331

Mathematical Reviews number (MathSciNet)
MR3781430

Zentralblatt MATH identifier
06861676

#### Citation

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. https://projecteuclid.org/euclid.akt/1522807265

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