A Fundamental Theorem for the $K$-theory of connective $\mathbb{S}$-algebras

Abstract

Invoking the density argument of Dundas-Goodwillie-McCarthy, we extend the Fundamental Theorem of $K$-theory from the category of simplicial rings to the category of $\mathbb{S}$-algebras. As an intermediate step, we prove the Fundamental Theorem for simplicial rings appealing to recent results from the first author's thesis. This recovers as a special case the Fundamental Theorem for the $K$-theory of spaces appearing in Hüttemann-Klein-Vogell-Waldhausen-Williams.

Revised and slightly restructured. 18 pages

References in corpus (1)

• Weight structures and the algebraic $K$-theory of stable $\infty$-categories

Cited by in corpus (1)

• The "fundamental theorem" for the algebraic $K$-theory of strongly $\mathbb{Z}$-graded rings