The motivic Adams conjecture

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.

v1: 24 pages; v2: 26 pages, final version to appear in the Journal of Topology, updated exposition, removed the inversion of the exponential characteristic in most places, added the discussion of the singular case,