Algebraic Kasparov K-theory. I

Grigory Garkusha

arxiv: 1004.0918 · v5 · pith:YLFLLHDMnew · submitted 2010-04-06 · 🧮 math.KT · math.AT· math.OA· math.RA

Algebraic Kasparov K-theory. I

Grigory Garkusha This is my paper

classification 🧮 math.KT math.ATmath.OAmath.RA

keywords stablealgebraicbivariantkasparovmoritaspectratheoriesunstable

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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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Algebraic Kasparov K-theory. I

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