STABLE COHOMOLOGY OVER LOCAL RINGS

Abstract. For a commutative noetherian ring R with residue eld k stable cohomology modules dExtn R (k; k) have been dened for each n 2 Z, but their meaning has remained elusive. It is proved that the k-rank of any dExtn R (k; k) characterizes important properties of R, such as being regular, complete inter-section, or Gorenstein. These numerical characterizations are based on results concerning the structure of Z-graded k-algebra carried by stable cohomology. It is shown that in many cases it is determined by absolute cohomology through a canonical homomorphism of algebras Ext R (k; k) ! dExt