A note on product structures on Hochschild homology of schemes
Volume 123 / 2011
Colloquium Mathematicum 123 (2011), 233-238
MSC: Primary 19D55; Secondary 18G60.
DOI: 10.4064/cm123-2-7
Abstract
We extend the definition of Hochschild and cyclic homologies of a scheme over a commutative ring $k$ to define the Hochschild homologies ${\rm HH}_*(X/S)$ and cyclic homologies ${\rm HC}_*(X/S)$ of a scheme $X$ with respect to an arbitrary base scheme $S$. Our main purpose is to study product structures on the Hochschild homology groups ${\rm HH}_*(X/S)$. In particular, we show that ${\rm HH}_*(X/S) =\bigoplus_{n\in \mathbb Z}{\rm HH}_n(X/S)$ carries the structure of a graded algebra.
