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

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.

Final version (to appear in Ann. K-Theory)

References in corpus (1)

• The six operations in equivariant motivic homotopy theory

Cited by in corpus (4)

• A moving lemma for algebraic cycles with modulus and contravariance
• Topological models for stable motivic invariants of regular number rings
• Nisnevich local Good compactifications
• A Nisnevich Local Bloch-Ogus Theorem over a General Base