Motivic Eilenberg--Mac Lane spaces at the characteristic
Abstract
We provide a novel, homotopy theoretic model for the motivic Eilenberg--Mac Lane spaces K(Z(p)(n), 2n) ∈ Spc(k) over fields of characteristic p. Using this, we determine their motives and, consequently, determine the motivic Steenrod algebra at the characteristic. Applications include the Hopkins--Morel isomorphism over arbitrary base schemes as well as the computation of the p-completed motivic stable stems and algebraic cobordism groups of fields of characteristic p. Along the way we expand the theory of normed algebraic structures in motivic homotopy theory, compare them to derived algebra at the characteristic, and produce a functor computing the motivic homology of the P1-loop spaces of (certain) motivic spaces in terms of the motives.
Related
- ℂ-Motivic Eilenberg-Mac Lane Spectra as MGL-Motivic Thom Spectra and Normed 𝔾m-Hochschild Homology
- A complete classification of the rational realization of gap-two products of Eilenberg--MacLane spaces as classifying spaces
- Parahoric motivic Hecke categories in equal and mixed characteristic
- Eilenberg-MacLane spaces in A-homotopy theory
- On The Rational Realization of Even-dimensional Spheres and Products of Eilenberg--MacLane Spaces as Classifying Spaces
BibTeX
@misc{bachmann2026motivic,
title = {{Motivic Eilenberg--Mac Lane spaces at the characteristic}},
author = {Tom Bachmann and Michael J. Hopkins},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02320},
eprint = {2611.02320},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02320},
}
RIS
TY - UNPB
TI - Motivic Eilenberg--Mac Lane spaces at the characteristic
AU - Tom Bachmann
AU - Michael J. Hopkins
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02320
UR - https://arxiv.org/abs/2611.02320
AB - We provide a novel, homotopy theoretic model for the motivic Eilenberg--Mac Lane spaces K(Z_(p)(n), 2n) ∈ Spc(k) over fields of characteristic p. Using this, we determine their motives and, consequently, determine the motivic Steenrod algebra at the characteristic. Applications include the Hopkins--Morel isomorphism over arbitrary base schemes as well as the computation of the p-completed motivic stable stems and algebraic cobordism groups of fields of characteristic p. Along the way we expand the theory of normed algebraic structures in motivic homotopy theory, compare them to derived algebra at the characteristic, and produce a functor computing the motivic homology of the P^1-loop spaces of (certain) motivic spaces in terms of the motives.
ER -