Weakly \(d\)-Koszul modules. (Q879687)

The paper under review deals with the so called weakly \(d\)-Koszul property. This is an obvious common generalization of the weakly-Koszul and \(d\)-Koszul properties. The graded modules with the latter property and generated in a single degree admit a cohomological characterization: their Ext-modules, viewed as modules over the Yoneda algebra, are generated in degree zero. The main result of the paper extends this characterization to weakly \(d\)-Koszul modules. The statement is similar to the just mentioned result, except that the Ext-module of the module should be replaced by that of the associated graded module. The authors also show that the Ext-module of a weakly \(d\)-Koszul module is finitely generated as a module over the Yoneda algebra.