Stable motivic trivial fibre decomposition over integers and framed motives

TL;DR

This paper explores the use of the trivial fiber topology to describe motivic $$-loop spaces and fibrant replacements within the motivic stable homotopy category over one-dimensional base schemes, advancing the understanding of motivic homotopy theory.

Contribution

It introduces a novel approach using the trivial fiber topology to analyze motivic $$-loop spaces and fibrant replacements over one-dimensional schemes.

Findings

Describes motivic $$-loop spaces using trivial fiber topology

Provides fibrant replacements in the motivic stable homotopy category

Enhances methods for studying motivic homotopy over schemes

Abstract

Using the trivial fiber topology we describe motivic $\infty$-loop spaces and fibrant replacements in the motivic stable homotopy category $\mathbf{SH}_{\mathbb{A}^1,\mathrm{Nis}}(B)$ defined over one-dimensional base schemes $B$.