The motivic Adams conjecture
K-Theory and Homology
2025-05-09 v2 Algebraic Geometry
Algebraic Topology
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.
Cite
@article{arxiv.2310.00974,
title = {The motivic Adams conjecture},
author = {Alexey Ananyevskiy and Elden Elmanto and Oliver Röndigs and Maria Yakerson},
journal= {arXiv preprint arXiv:2310.00974},
year = {2025}
}
Comments
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,