 
Summary: STABLE COHOMOLOGY OVER LOCAL RINGS
LUCHEZAR L. AVRAMOV AND OANA VELICHE
Abstract. For a commutative noetherian ring R with residue field k stable
cohomology modules dExtn
R(k, k) have been defined for each n Z, but their
meaning has remained elusive. It is proved that the krank 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 Zgraded kalgebra carried by stable cohomology.
It is shown that in many cases it is determined by absolute cohomology through
a canonical homomorphism of algebras ExtR(k, k) dExtR(k, k). Some tech
niques developed in the paper are applicable to the study of stable cohomology
functors over general associative rings.
Contents
Introduction 1
1. Cohomology theories 3
2. Comparisons 6
3. Additional structures 8
4. Nonzerodivisors 11
