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

TL;DR

This paper investigates how $\

Contribution

It establishes a Nisnevich-local version of Gabber's geometric presentation lemma over Dedekind schemes, advancing understanding of $\

Findings

$\

$\

$\

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.