The trivial fiber topology and framed motives over the integers

2020/12/14 by A. Druzhinin, Druzhinin, A., Håkon Kolderup +3 · 1 citation
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2012.07365

Abstract

This paper introduces the trivial fiber topology on schemes. For one-dimensional base schemes, we use it to describe fibrant replacements in the stable motivic homotopy category and motivic infinite loop spaces. We also extend the Garkusha-Panin and Voevodsky strict \mathbbA¹-invariance theorems to one-dimensional base schemes. The trivial fiber topology plays a central role in the proof of refined localization results for motivic homotopy categories. Moreover, we extend Morel's \mathbbA¹-connectivity theorem on Nisnevich sheaves of stable motivic homotopy groups. These results open new vistas for computations of motivic invariants over deeper base schemes of arithmetic interest.

Cited by

• Zariski-local framed \mathbbA¹-homotopy theory

Related

• Stable motivic trivial fibre decomposition over integers and framed motives
• Strict homotopy invariance via compactified homotopies and correspondences, and fibres of essentially smooth schemes over one-dimensional base schemes
• Framed motivic Γ-spaces
• Framed motives of algebraic varieties (after V. Voevodsky)
• Framed motives of smooth affine pairs