A Fundamental Theorem for the K-theory of connective\n mathbbS-algebras

2018/03/30 by Ernest E. Fontes, Fontes, Ernest E., Crichton Ogle +1
Mathematics · #19D35 #19Dxx #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1804.00975

openalex publication_date 2018/03/30 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

Invoking the density argument of Dundas-Goodwillie-McCarthy, we extend the\nFundamental Theorem of K-theory from the category of simplicial rings to the\ncategory of mathbbS-algebras. As an intermediate step, we prove the\nFundamental Theorem for simplicial rings appealing to recent results from the\nfirst author's thesis. This recovers as a special case the Fundamental Theorem\nfor the K-theory of spaces appearing in\nH "uttemann-Klein-Vogell-Waldhausen-Williams.\n

Citations

• Weight structures and the algebraic K-theory of stable ∞-categories

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