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Remarks on chromatically localised hermitian K-theory

· 2022 · math.KT · DOI 10.48550/arxiv.2202.05036 · arXiv 2202.05036

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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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math.KT 1

years

2025 1

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  • Chromatic Purity in Hermitian K-Theory at $p=2$ math.KT · 2025-01-16 · reject · none · ref 13 · internal anchor

    At p=2, L-theory of rings with anti-involution is claimed to have no chromatic redshift and to satisfy a chromatic purity theorem.