The motivic Adams conjecture

TL;DR

This paper proves a motivic version of the Adams conjecture, introduces related theorems, and analyzes the properties of motivic stable stems, advancing the understanding of algebraic topology in a motivic setting.

Contribution

It provides the first proof of a motivic Adams conjecture and develops new motivic theorems, including a motivic Dold theorem and analysis of stable stems.

Findings

Motivic Adams conjecture is proven with inverted exponential characteristic.

Motivic version of mod k Dold theorem established.

Higher motivic stable stems are shown to have bounded torsion.

Abstract

We solve a motivic version of the Adams conjecture with the exponential characteristic of the base field inverted. In the way of the proof we obtain a motivic version of mod k Dold theorem and give a motivic version of Brown's trick studying the homogeneous variety of maximal tori in a general linear group, which turns out to be not stably A1-connected. We also show that the higher motivic stable stems are of bounded torsion.