Kerz, Moritz; Saito, Shuji; Tamme, Georg

\(K\)-Theory of Non-Archimedean Rings. I

Doc. Math. 24, 1365-1411 (2019)
DOI: 10.25537/dm.2019v24.1365-1411
Communicated by Max Karoubi

Summary

We introduce a variant of homotopy \(K\)-theory for Tate rings, which we call \textit{analytic \(K\)-theory}. It is homotopy invariant with respect to the analytic affine line viewed as an ind-object of closed disks of increasing radii. Under a certain regularity assumption we prove an analytic analog of the Bass fundamental theorem and we compare analytic \(K\)-theory with continuous \(K\)-theory, which is defined in terms of models. Along the way we also prove some results about the algebraic \(K\)-theory of Tate rings.

Mathematics Subject Classification

19D25, 14G22

Keywords/Phrases

continuous \(K\)-theory, affinoid algebras

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Affiliation

Kerz, Moritz
Fakult\``at f\''ur Mathematik, Universit\``at Regensburg, 93040 Regensburg, Germany
Saito, Shuji
Graduate School of Mathematical, Sciences University of Tokyo, 3-8-1 Komaba, Tokyo, Japan
Tamme, Georg
Fakult\''at f\``ur Mathematik, Universit\''at Regensburg, 93040 Regensburg, Germany

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