Geodesic
A note on product structures on Hochschild homology of schemes
Abhishek Banerjee1
1 Department of Mathematics Ohio State University 231 W 18th Avenue Columbus, OH 43210, U.S.A.
Colloquium Mathematicum, Tome 123 (2011) no. 2, pp. 233-238

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm123-2-7
Keywords: extend definition hochschild cyclic homologies scheme commutative ring define hochschild homologies * cyclic homologies * scheme respect arbitrary base scheme main purpose study product structures hochschild homology groups * particular * bigoplus mathbb carries structure graded algebra

Abhishek Banerjee 1

1 Department of Mathematics Ohio State University 231 W 18th Avenue Columbus, OH 43210, U.S.A. 
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Abhishek Banerjee. A note on product structures on Hochschild homology of schemes. Colloquium Mathematicum, Tome 123 (2011) no. 2, pp. 233-238. doi: 10.4064/cm123-2-7

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