K-theory of non-archimedean rings I

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.

arXiv comment43 pages, final version

References in corpus (7)

• Higher Topos Theory
• Desingularization of quasi-excellent schemes in characteristic zero
• Towards a non-archimedean analytic analog of the Bass-Quillen conjecture
• Relative continuous K-theory and cyclic homology
• An Open Mapping Theorem for rings which have a zero sequence of units
• A historical overview of pro cdh descent in algebraic $K$-theory and its relation to rigid analytic varieties
• Continuous K-Theory and Cohomology of Rigid Spaces

Cited by in corpus (1)

• Non-archimedean quantum K-invariants