On the algebraic K-theory of formal power series

Ayelet Lindenstrauss, Randy McCarthy

Research output: Contribution to journalArticlepeer-review


In this paper we extend the computation of the the typical curves of algebraic K-theory done by Lars Hesselholt and Ib Madsen to general tensor algebras. The models used allow us to determine the stages of the Taylor tower of algebraic K-theory as a functor of augmented algebras, as defined by Tom Goodwillie, when evaluated on derived tensor algebras. For R a discrete ring, and M a simplicial R-bimodule, we let R(M) denote the (derived) tensor algebra of M over R, and π R(M) denote the ring of formal (derived) power series in M over R. We define a natural transformation of functors of simplicial R-bimodules Î which is closely related to Waldhausen's equivalence We show that φ induces an equivalence on any finite stage of Goodwillie's Taylor towers of the functors at any simplicial bimodule. This is used to show that there is an equivalence of functors , and for connected bimodules, also an equivalence

Original languageEnglish (US)
Pages (from-to)165-189
Number of pages25
JournalJournal of K-Theory
Issue number1
StatePublished - Aug 2012


  • Formal Power Series
  • Goodwillie Calculus
  • K-theory of Endomorphisms
  • Key Words Algebraic K-theory
  • Tensor Algebra

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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