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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