A Fundamental Theorem for the $K$-theory of connective $\mathbb{S}$-algebras
K-Theory and Homology
2020-04-21 v4 Algebraic Topology
Abstract
Invoking the density argument of Dundas-Goodwillie-McCarthy, we extend the Fundamental Theorem of -theory from the category of simplicial rings to the category of -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 -theory of spaces appearing in H\"uttemann-Klein-Vogell-Waldhausen-Williams.
Cite
@article{arxiv.1804.00975,
title = {A Fundamental Theorem for the $K$-theory of connective $\mathbb{S}$-algebras},
author = {Ernest E. Fontes and Crichton Ogle},
journal= {arXiv preprint arXiv:1804.00975},
year = {2020}
}
Comments
Revised and slightly restructured. 18 pages