Fundamental theorems for the K-theory of $\mathbf{S}$-algebras, I: the connective case

Abstract

We extend the Bass-Quillen Fundamental Theorem of Algebraic K-theory to the Waldhausen K-theory of connective $\mathbf{S}$-algebras. The same technique used in this extension also yields two localization theorems for the relative K-theory of a 1-connected morphism of connective $\mathbf{S}$-algebras.

This update contains an improvement on Theorem 2. This is the first part of a series

References in corpus (2)

• Localization theorems in topological Hochschild homology and topological cyclic homology
• On the Taylor Tower of Relative K-theory