Algèbre non commutative, groupes quantiques et invariants Septième contact Franco-Belge, Reims, Juin 1995
J. Alev, G. Cauchon (Éd.)
Séminaires et Congrès 2 (1997), 304 pages
Schematic Algebras and the Auslander-Gorenstein Property
Séminaires et Congrès 2 (1997), 149-156
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Noncommutative algebraic geometry studies a certain quotient category R-qgr of the category of graded R-modules which for commutative R is equivalent to the category of quasi-coherent sheaves by a famous theorem of Serre. For a large class of graded algebras, the so-called schematic algebras, we are able to construct a kind of scheme such that the coherent sheaves on it are equivalent to R-qgr. We give a brief survey on the results so-far on schematic algebras and include some new results on cohomological properties of Auslander-Gorenstein algebras which might be useful in determining the strength of the schematic property.
Class. math. : 14A15, 14A22, 16E40, 16W50