Algebraic Kasparov K-theory. I

Details Algebraic Kasparov K-theory. I Algebraic Kasparov K-theory. I

2010-04-06

arxiv.org/abs/1004.0918v4

Mathematics

K-Theory and Homology

Proposition 4.1 does not work for fibrations being all surjective homomorphisms. Only because of this difficulty spectra repre

Scientific paper

This paper is to construct bivariant versions of algebraic K-theory. Unstable, Morita stable and stable bivariant algebraic Kasparov K-theory spectra of k-algebras are introduced. 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 introduced by the author. Also, unstable, Morita stable and stable algebraic K-theory spectra of k-algebras as well as their dual unstable, Morita stable and stable K-cohomology spectra are introduced. These are shown to be homotopy invariant, excisive K-theories/K-cohomologies. It is proved that there is an isomorphism between stable K-theory groups and homotopy algebraic K-theory groups in the sense of Weibel.

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