Homological properties of commutative noetherian rings, such as being regular, Cohen-Macaulay, or Gorenstein, are defined locally at every maximal ideal. For a finitely generated algebra $S$ over a field $K$ the first two properties can be recognized by means of easily applicable criteria. It will be shown in the talk that when $S$ is a Cohen-Macaulay domain, it is Gorenstein if and only if the Hochschild cohomology modules $\operatorname{Ext}^n_{S\otimes_K S}(S,{S\otimes_K S})$ vanish for
$\dim S formulas for Hochschild cohomology.
The talk is based on joint work with Srikanth Iyengar.

Lecture #13401

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