Geodesic
$K$-Theory of Non-Archimedean Rings. I
Documenta mathematica, Tome 24 (2019), pp. 1365-1411.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 19D25, 14G22
Keywords: continuous \(K\)-theory, affinoid algebras 
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     author = {Kerz, Moritz and Saito, Shuji and Tamme, Georg},
     title = {\(K\)-Theory of {Non-Archimedean} {Rings.} {I}},
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Kerz, Moritz; Saito, Shuji; Tamme, Georg. \(K\)-Theory of Non-Archimedean Rings. I. Documenta mathematica, Tome 24 (2019), pp. 1365-1411. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a28/