Algebraic Kasparov $K$-theory. I

Grigory Garkusha

doi:10.4171/dm/479

JournalsdmVol. 19pp. 1207–1269

Algebraic Kasparov $K$ -theory. I

Grigory Garkusha
Department of Mathematics Swansea University Singleton Park Swansea SA2 8PP United Kingdom

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Abstract

This paper is to construct unstable, Morita stable and stable bivariant algebraic Kasparov $K$ -theory spectra of $k$ -algebras. These are shown to be homotopy invariant, excisive in each variable $K$ -theories. We prove that the spectra represent universal unstable, Morita stable and stable bivariant homology theories respectively.

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Grigory Garkusha, Algebraic Kasparov $K$ -theory. I. Doc. Math. 19 (2014), pp. 1207–1269

DOI 10.4171/DM/479