# Motivic stable homotopy theory is strictly commutative at the characteristic

@article{Bachmann2021MotivicSH,
title={Motivic stable homotopy theory is strictly commutative at the characteristic},
author={Tom Bachmann},
year={2021}
}
• Tom Bachmann
• Published 3 November 2021
• Mathematics

## References

SHOWING 1-10 OF 58 REFERENCES

. We show that if G is a ﬁnite constant group acting on a scheme X such that | G | ∈ O × X , then the G -equivariant motivic stable homotopy category of X is equivalent to the stabilization of the

### Remarks on \'etale motivic stable homotopy theory

• 2021
• Mathematics
• 2021
. We deﬁne a notion of colimit for diagrams in a motivic category indexed by a presheaf of spaces (e.g. an ´etale classifying space), and we study basic properties of this construction. As a case
1.1. A motivating example: elliptic cohomology theories. Generalized cohomology theories are functors which take values in some abelian category. Traditionally, we consider ones which take values in
• Mathematics
Mathematische Annalen
• 2020
We give necessary and sufficient conditions for a cdh sheaf to satisfy Milnor excision, following ideas of Bhatt and Mathew. Along the way, we show that the cdh ∞\documentclass[12pt]{minimal}
• Mathematics
• 2020
Over any field of characteristic not 2, we establish a 2-term resolution of the $\eta$-periodic, 2-local motivic sphere spectrum by shifts of the connective 2-local Witt K-theory spectrum. This is
• Mathematics
• 2019
We obtain geometric models for the infinite loop spaces of the motivic spectra $\mathrm{MGL}$, $\mathrm{MSL}$, and $\mathbf{1}$ over a field. They are motivically equivalent to $\mathbb{Z}\times • Mathematics Forum of Mathematics, Pi • 2020 Abstract We prove that the$\infty $-category of$\mathrm{MGL} $-modules over any scheme is equivalent to the$\infty $-category of motivic spectra with finite syntomic transfers. Using the • Mathematics • 2019 We establish a motivic version of the May Nilpotence Conjecture: if E is a normed motivic spectrum that satisfies$E \wedge HZ \simeq 0$, then also$E \wedge MGL \simeq 0\$. In words, motivic homology
• Mathematics
Inventiones mathematicae
• 2021
We study the étale sheafification of algebraic K-theory, called étale K-theory. Our main results show that étale K-theory is very close to a noncommutative invariant called Selmer K-theory, which is