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K-theory of non-archimedean rings II

Moritz Kerz, Shuji Saito, Georg Tamme

Abstract

We study fundamental properties of analytic $K$-theory of Tate rings such as homotopy invariance, Bass fundamental theorem, Milnor excision, and descent for admissible coverings.

K-theory of non-archimedean rings II

Abstract

We study fundamental properties of analytic -theory of Tate rings such as homotopy invariance, Bass fundamental theorem, Milnor excision, and descent for admissible coverings.

Paper Structure

This paper contains 9 sections, 16 theorems, 73 equations.

Table of Contents

  1. Introduction
  2. Recollections from part I, and complements
  3. Pro-homotopy algebraic $K$-theory
  4. The fundamental fibre sequence
  5. Excision for analytic $K$-theory
  6. Descent and applications
  7. Descent for analytic K-theory
  8. Globalization
  9. Properties of analytic K-theory

Key Result

Lemma 2.2

For $X \in \mathbf{Sch}_{R}$ the canonical map is an equivalence of pro-spectra. Similarly for $K^{\pi^{\infty}}(- \,\mathrm{on}\, (\pi))$.

Theorems & Definitions (37)

  • Definition 2.1
  • Lemma 2.2
  • Lemma 2.3
  • proof
  • Theorem 2.4
  • Example 2.5
  • proof : Proof of Theorem \ref{['thm.weakfibresequence']}
  • Corollary 2.6: Bass fundamental theorem for analytic $K$-theory
  • proof
  • Corollary 2.7: Pro-homotopy invariance
  • ...and 27 more