The Taylor towers for rational algebraic $K$-theory and Hochschild homology

We compute the Taylor tower for Hochschild homology as a functor from augmented commutative simplicial $\mathbb{Q}$-algebras, to chain complexes over $\mathbb{Q}$. We use this computation to obtain the layers for the Taylor tower of rational algebraic $K$-theory. We also show that the Hodge decomposition for rational Hochschild homology is the decomposition of the Taylor tower of the augmentation ideal functor into its homogeneous layers when evaluated at a suspension.

Keywords

Goodwillie calculus, Rational algebraic $K$-theory, Hochschild homology, Hodge decomposition

2010 Mathematics Subject Classification

13D03, 19D55, 55Uxx

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Published 1 January 2002