Koszul Modules

This paper studies a new class of modules over noetherian local rings, called Koszul modules. It is proved that when a Koszul local ring R is a complete intersection, all high syzygies of finitely generated R-modules are Koszul. A stronger result is obtained when R is Golod and of embedding dimension d: the 2dth syzygy of every R-module is Koszul. In addition, results are established that demonstrate that Koszul modules possess good homological properties; for instance, their Poincaré series is a rational function.