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STABLE COHOMOLOGY OVER LOCAL RINGS LUCHEZAR L. AVRAMOV AND OANA VELICHE
 

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 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 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. Non-zero-divisors 11

  

Source: Avramov, Luchezar L.- Department of Mathematics, University of Nebraska-Lincoln

 

Collections: Mathematics