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arXiv · 2307.13512

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

William Balderrama·Kyle Ormsby·J. D. Quigley
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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.

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BibTeXRIS

William Balderrama, Kyle Ormsby, J. D. Quigley. 2023-07-25. A motivic analogue of the K(1)-local sphere spectrum. https://arxiv.org/abs/2307.13512

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