Conditions for the Yoneda algebra of a local ring to be generated in low degrees

Abstract The powers m n of the maximal ideal m of a local Noetherian ring R are known to satisfy certain homological properties for large values of n . For example, the homomorphism R → R / m n is Golod for n ≫ 0 . We study when such properties hold for small values of n , and we make connections with the structure of the Yoneda Ext algebra, and more precisely with the property that the Yoneda algebra of R is generated in degrees 1 and 2. A complete treatment of these properties is pursued in the case of compressed Gorenstein local rings.