Abstract :
Let A be a noetherian AS-regular Koszul quiver algebra (if A is commutative, it is essentially a polynomial ring), and image the category of finitely generated graded left A-modules. Following Jørgensen, we define the Castelnuovo–Mumford regularity image of a complex image in terms of the local cohomologies or the minimal projective resolution of M•. Let A! be the quadratic dual ring of A. For the Koszul duality functor image, we have image. Using these concepts, we interpret results of Martinez-Villa and Zacharia concerning weakly Koszul modules (also called componentwise linear modules) over A!. As an application, refining a result of Herzog and Römer, we show that if J is a monomial ideal of an exterior algebra E=logical or operatorleft angle brackety1,…,ydright-pointing angle bracket, d≥3, then the (d−2)nd syzygy of E/J is weakly Koszul.
