Schematic Algebras and the Auslander-Gorenstein Property
Schematic Algebras and the Auslander-Gorenstein Property
Séminaires et Congrès | 1997
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- Année : 1997
- Tome : 2
- Format : Papier
- Langue de l'ouvrage :
Anglais - Class. Math. : 14A15, 14A22, 16E40, 16W50
- Pages : 149-156
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 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.