Abstract
The first goal of this chapter is to prove that the three different constructions commonly used for algebraic K-theory, namely Quillen’s plus, Waldhausen’s S-construction and Segal’s Γ-space construction are suitably equivalent.
The second goal of this chapter is to use the interplay of these equivalent models to make two reductions. One reduction transfers a wide range of problems on the algebraic K-theory of strictly associative ring spectra to simplicial rings while another reduction transfers some rather special problems of the algebraic K-theory of simplicial rings to discrete rings.
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Dundas, B.I., Goodwillie, T.G., McCarthy, R. (2013). Reductions. In: The Local Structure of Algebraic K-Theory. Algebra and Applications, vol 18. Springer, London. https://doi.org/10.1007/978-1-4471-4393-2_3
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