Work

A motivic analogue of the $K(1)$-local sphere spectrum

Year: 2025

Type: article

Abstract: We identify the motivic KGL/2 -local sphere as the fiber of \psi^{3}-1 on (2,\eta) -completed Hermitian K -theory, over any base scheme containing 1/2 . This is a motivic analogue of the classical resolution of the K(1) -local sphere, and extends to a description of the KGL/2 -localization of an arbitrary motivic spectrum. Our proof relies on a novel conservativity argument that should be of broad utility in stable motivic homotopy theory.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1641

Authors: William Balderrama, Kyle Ormsby, James D. Quigley

Institutions: University of Virginia, Reed College

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4409164276

FWCI: 1.636

Cites:

Cited by: 1

Related to: 10