Co-point modules over Koszul algebras

• Autores: Izuru Mori
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 74, Nº 3, 2006, págs. 639-656
• Idioma: inglés
• DOI: 10.1112/s002461070602326x
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• Resumen

  • Let $A$ be a graded algebra finitely generated in degree 1 over a field $k$. Point modules over $A$ introduced by Artin, Tate and Van den Bergh play an important role in studying $A$ in noncommutative algebraic geometry. In this paper, we define a dual notion of point module in terms of Koszul duality, which we call a co-point module. Using co-point modules, we will construct counter-examples to the following condition due to Auslander: for every finitely generated right module $\pi$ over a ring $R$, there is a natural number $n_M\in {\mathbb N}$ such that, for any finitely generated right module $N$ over $R$, ${\rm Ext}^i_R(M, N)=0$ for all $i\gg 0$ implies ${\rm Ext}^i_R(M, N)=0$ for all $i>n_M$.