DOCUMENTA MATHEMATICA, Vol. 19 (2014), 1207-1269

Grigory Garkusha

Algebraic Kasparov K-theory. I

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.

2010 Mathematics Subject Classification: 19D99, 19K35, 55P42

Keywords and Phrases: Bivariant algebraic K-theory, homotopy theory of algebras, triangulated categories

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