# Hochschild (co-)homology of schemes with tilting object

@inproceedings{Buchweitz2010HochschildO, title={Hochschild (co-)homology of schemes with tilting object}, author={Ragnar-Olaf Buchweitz and Lutz Hille}, year={2010} }

Given a $k$--scheme $X$ that admits a tilting object $T$, we prove that the Hochschild (co-)homology of $X$ is isomorphic to that of $A= End_{X}(T)$. We treat more generally the relative case when $X$ is flat over an affine scheme $Y=\Spec R$ and the tilting object satisfies an appropriate Tor-independence condition over $R$. Among applications, Hochschild homology of $X$ over $Y$ is seen to vanish in negative degrees, smoothness of $X$ over $Y$ is shown to be equivalent to that of $A$ over $R… CONTINUE READING

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