Bivariant algebraic K-theory

By Guillermo Cortiñas, Andreas Thom. 2006

57 citations recorded by the source corpus.

Abstract We show how methods from K-theory of operator algebras can be applied in a completely algebraic setting to define a bivariant, M ∞-stable, homotopy-invariant, excisive K-theory of algebras over a fixed unital ground ring H, (A, B) ↦ kk *(A, B), which is universal in the sense that it maps uniquely to any other such theory. It turns out kk is related to C. Weibel's homotopy algebraic K-theory, KH. We prove that, if H is commutative and A is central as an H-bimodule, then We show further that some calculations from operator algebra KK-theory, such as the exact sequence of Pimsner-Voiculescu, carry over to algebraic kk.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a44baf279e608397a2ab8e1535df4e0e93a8d460

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Citations in the corpus

Higher K-theory via universal invariants (2007, result): “Our construction is similar in spirit to those of Meyer-Nest [29], Corti~ nas-Thom [ 8 ] and Garkusha [12].”
A universal characterization of higher algebraic K-theory (2010, background): “The “motivic” idea of constructing universal invariants is not new and appears in several different subjects: for example, Cortiñas-Thom’s work [11] on bivariant algebraic K-theory, Higson’s work [27] on Kasparov’s bivariant Ktheory, Meyer-Nest’s work [43] on C-algebras, Morel-Voevodsky’s work [41] ”