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Does a morphism which induces an isomorphism between Hochschild homology also induce an isomorphism between cyclic homology?

In a 1998 paper by B. Keller, the author consider the following problem in Section 1.4: Let $k$ be a commutative ring and $X$ a scheme over $k$. We can consider the cyclic homology as well as the ...
7 votes
1 answer
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What is the negative cyclic homology of a smooth projective variety?

Let X be a smooth and projective variety. Hochschild homology and cohomology have a very simple definition in terms of Ext groups of the diagonal of X. The Hochschild-Kostant-Rosenberg (HKR) theorem ...