The Künneth formula in periodic cyclic homology (Q1915495)

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.