The Künneth formula in periodic cyclic homology
type: Item
instance of: scholarly article
title: The Künneth formula in periodic cyclic homology
zbMATH Open document ID: 0847.19001
DOI: 10.1007/BF00536612
author: Ioannis Emmanouil
published in: \(K\)-Theory
publication date: 1996-10-08T00:00:00Z
review text: The author introduces a functor \({\mathcal H}\) defined on associative algebras; it is an integer-graded variant of periodic cyclic homology \(HP\). If \(A\) is a commutative algebra of finite type over a field \(k\) of characteristic zero, then \({\mathcal H} (A)\) is the infinitesimal cohomology of the spectrum of \(A\) over the spectrum of \(k\). The author investigates Künneth formulae. There is always an isomorphism \({\mathcal H} (A \otimes A') \cong {\mathcal H} (A) \otimes {\mathcal H} (A')\). As a consequence, given a fixed algebra \(A\), there are isomorphisms \(HP (A \otimes A') \cong HP (A) \otimes HP (A')\) for all \(A'\) if and only if \(A\) satisfies certain finiteness and Mittag-Leffler conditions.
reviewed by: Richard John Steiner
Mathematics Subject Classification ID: 19D55
Mathematics Subject Classification ID: 18G15
Mathematics Subject Classification ID: 18G60
zbMATH DE Number: 890734
zbMATH Keywords: Künneth isomorphism
zbMATH Keywords: periodic cyclic homology
zbMATH Keywords: infinitesimal cohomology
zbMATH Keywords: Künneth formula
MaRDI profile type: Publication
cites work: The Künneth formula in cyclic homology
cites work: Non-commutative differential geometry
cites work: Q4297381
cites work: Additive \(K\)-theory and crystalline cohomology
cites work: Cyclic homology, derivations, and the free loopspace
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cites work: Cyclic homology, comodules, and mixed complexes
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full work available at URL: https://doi.org/10.1007/bf00536612
OpenAlex ID: W2072049198
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description: scientific article; zbMATH DE number 890734