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arXiv · 1802.09819

K-theory of non-archimedean rings I

Moritz Kerz·Shuji Saito·Georg Tamme
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Abstract

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 models. Along the way we also prove some results about the algebraic K-theory of Tate rings.

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Moritz Kerz, Shuji Saito, Georg Tamme. 2018-02-27. K-theory of non-archimedean rings I. https://doi.org/10.25537/dm.2019v24.1365-1411

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