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We compute the Taylor tower for Hochschild homology as a functor from augmented commutative simplicial Q-algebras, to chain complexes over Q. We use this computation to obtain the layers for the Taylor tower of rational algebraic Ktheory. 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.

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