References
SHOWING 1-10 OF 58 REFERENCES
Motivic spectral Mackey functors
- Mathematics
- 2022
. 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
Motivic colimits and extended powers
- 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…
SPECTRAL ALGEBRAIC GEOMETRY
- Mathematics
- 2020
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…
Cdh descent, cdarc descent, and Milnor excision
- MathematicsMathematische 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}…
$\eta$-periodic motivic stable homotopy theory over fields
- 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…
On the infinite loop spaces of algebraic cobordism and the motivic sphere
- 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…
Modules over algebraic cobordism
- MathematicsForum 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…
Nilpotence in normed MGL-modules
- 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…
Hyperdescent and étale K-theory
- MathematicsInventiones 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…