Geodesic
$K$-Theory of Non-Archimedean Rings. I
Documenta mathematica, Tome 24 (2019), pp. 1365-1411
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We introduce a variant of homotopy K-theory for Tate rings, which we call 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.
DOI : 10.4171/dm/707
Classification : 14G22, 19D25
Mots-clés : affinoid algebras, continuous K-theory 
@article{10_4171_dm_707,
     author = {Moritz Kerz and Georg Tamme and Shuji Saito},
     title = {$K${-Theory} of {Non-Archimedean} {Rings.} {I}},
     journal = {Documenta mathematica},
     pages = {1365--1411},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/707},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/707/}
}
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Moritz Kerz; Georg Tamme; Shuji Saito. $K$-Theory of Non-Archimedean Rings. I. Documenta mathematica, Tome 24 (2019), pp. 1365-1411. doi: 10.4171/dm/707

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