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Remarks on chromatically localised hermitian K-theory

Published 10 Feb 2022 in math.KT and math.AT | (2202.05036v1)

Abstract: We describe chromatic localisations of genuine L-spectra of discrete rings and deduce that the purity property of $K(1)$-local $K$-theory of rings established by Bhatt-Clausen-Mathew also holds in Grothendieck-Witt theory. In addition, we collect some results on higher chromatic localisations of various L-theory spectra and their consequences for Grothendieck-Witt theory.

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