Continuous K-theory of rigid analytic spaces is a Nisnevich sheaf, and, after A1-localization, it is represented by Z x BGL under a resolution-of-singularities assumption.
Weibel.K-theory and analytic isomorphisms.Invent
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Representability of continuous K-theory in rigid analytic motivic $\mathbb{A}^1$-homotopy theory
Continuous K-theory of rigid analytic spaces is a Nisnevich sheaf, and, after A1-localization, it is represented by Z x BGL under a resolution-of-singularities assumption.