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Advances in Algebra and Geometry |
| April 28, 2007 to May 04, 2007 |
| Organized By: David Ellwood, Joe Harris, Craig Huneke, Hugo Rossi, Frank-Olaf Schreyer, Bernd Sturmfels, Julius Zelmanowitz |
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| Return to Workshop Description |
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Finitistic global criteria for the Gorenstein property
Tuesday May 1, 2007
02:00PM - 03:00PM
Speakers:
Luchezar Avramov
Abstract:
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
$\dim S<n\le 2\dim S$. Similar results hold also in more general, relative situations. The proofs involve surprising reduction
formulas for Hochschild cohomology.
The talk is based on joint work with Srikanth Iyengar.
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